Optimal

optimal

Table of Links Abstract and 1 Introduction 2 Preliminaries 3 Temporal Hierarchies 4 Rating Maps 5 Optimal Imprints for TL(AT) 6 Conclusion and References Appendix A. Appendix to Section 2 & Appendix B. Appendix to Section 3 Appendix C. Appendix to Section 4 & Appendix D. Appendix to Section 5 5. Optimal imprints for TL(AT) This paper is available on arxiv under CC BY 4.0 DEED license. Authors:
(1) Thomas Place;
(2) Marc Zaitoun. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Preliminaries 2 Preliminaries 3 Temporal Hierarchies 3 Temporal Hierarchies 4 Rating Maps 4 Rating Maps 5 Optimal Imprints for TL(AT) 5 Optimal Imprints for TL(AT) 6 Conclusion and References 6 Conclusion and References Appendix A. Appendix to Section 2 & Appendix B. Appendix to Section 3 Appendix A. Appendix to Section 2 & Appendix B. Appendix to Section 3 Appendix C. Appendix to Section 4 & Appendix D. Appendix to Section 5 Appendix C. Appendix to Section 4 & Appendix D. Appendix to Section 5 5. Optimal imprints for TL(AT) This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv Authors: (1) Thomas Place; (2) Marc Zaitoun. Authors: Authors: (1) Thomas Place; (2) Marc Zaitoun.

Optimal Imprints for TL(AT): Explaining Our Main Theorem

Authors:
(1) Jongmin Lee, Department of Mathematical Science, Seoul National University;
(2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction 1.1 Notations and preliminaries 1.2 Prior works 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 4 Complexity lower bound 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries B Omitted proofs in Section 2 C Omitted proofs in Section 3 D Omitted proofs in Section 4 E Omitted proofs in Section 5 F Omitted proofs in Section 6 G Broader Impacts H Limitations A Preliminaries For notational unity, we use the symbol U when both V and Q can be used. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Authors: Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Notations and preliminaries 1.1 Notations and preliminaries 1.2 Prior works 1.2 Prior works 2 Anchored Value Iteration 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 3 Convergence when y=1 4 Complexity lower bound 4 Complexity lower bound 5 Approximate Anchored Value Iteration 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries A Preliminaries B Omitted proofs in Section 2 B Omitted proofs in Section 2 C Omitted proofs in Section 3 C Omitted proofs in Section 3 D Omitted proofs in Section 4 D Omitted proofs in Section 4 E Omitted proofs in Section 5 E Omitted proofs in Section 5 F Omitted proofs in Section 6 F Omitted proofs in Section 6 G Broader Impacts G Broader Impacts H Limitations H Limitations A Preliminaries For notational unity, we use the symbol U when both V and Q can be used. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Foundational Lemmas for Bellman Optimality and Anti-Optimality Operators

This is Part 6 of a 7-part series of the research paper “Towards Usability Guidelines for the Design of Effective Arabic Websites”. Use the table of links below to navigate to the other parts. Table of Links Abstract and I. Introduction II. Previous Works III. Research Methodology IV. Font and Image Inspection Studies V. Results VI. Discussion VII. Conclusions, Future Research Directions, and References VI. DISCUSSION Our comprehensive inspection of current practices concerning text formatting and image usage within the top visited Arabic websites in Saudi Arabia revealed various interesting findings. The usability inspection was performed to gather insights about the font types and sizes used to style Arabic text, especially that they could directly influence the legibility of text on websites. Let us review and attempt to answer the research questions posited in the introduction. What font types and font sizes are used by major Arabic websites? On the positive side, the selection of the Arabic websites included a large pool of websites, which were selected objectively by relying on Alexa Internet latest ranking. In effect, the inspection covered a total of 73 top viewed websites (52 local and 21 international) in Saudi Arabia. The websites' ranking is based on a set of metrics, primarily the average viewing time for the last three months. Typically, a font has several characteristics including type, size, width, weight, and serifs [37], [46]. However, for the purpose of this research, we directed our focus towards two key font characteristics namely type and size. On the web, font type usually refers to the font family that represents a certain typeface, including all sizes and styles, for example, Arial and Verdana. To style a particular family type, the size of text may be increased or decreased using the font size attribute. There are different ways to resize the font including Ems (em), pixels (px), points (pt), and percent (%). In our font size analysis, we used pixels (px) as the sole measurement for the font since it is the main measurement unit for media shown on computer screens. Moreover, web designers usually use pixels as their key measurement unit for font size. Points, however, are used to measure font size for print media. It is noted that more than half of the Arabic websites breached the principle of consistency when applying font types to the text. This means that multiple font types were used on the same web pages. Previous research, however, has already emphasized the role of consistency of user interface elements, such as font, in the overall usability of websites [35], [36]. On that basis, it is recommended that designers should adhere to the same font family to create attractive and consistent Arabic web designs. Moreover, there was no evident consensus amongst the websites in favoring a particular font type in order to display the Arabic text. More than 35 font types were used by the selected 73 websites. There are various potential theories that could explain this staggering variability; firstly, the lack of research and thereby guidelines with respect to styling Arabic text to guide the effective design of Arabic websites; secondly, the weak conformance to international design practices and recommendations; thirdly, the lack of awareness that text formatting might ultimately impact text legibility and thereby readers' mental load and overall satisfaction. Nonetheless, a pattern of font usage emerged within the Arabic websites; six font types recurred several times in the formatting of titles/headline, menus, and paragraphs. These font types were used differently according to the type of text element. For titles and menus, Droid Arabic Kufi, Tahoma, Helvetica, and Arial, emerged as favorites. It is no surprise that Droid Arabic Kufi came out as a winner for it is a unique font that reflects the Arabic calligraphy. This font gives a true feeling of the traditional Arabic scripts (Kufic scripts) that date back to the 7th century. For paragraphs, Tahoma, Helvetica, Arial and Times New Roman were used more frequently. International recommendations suggest using font type Verdana since it is one of the most legible fonts as rated by online readers of English websites [38]. Nonetheless, this font did not appear frequently in the Arabic websites that we tested. Moreover, other famous fonts that were found earlier to be legible or attractive by English readers, such as Georgia [18] and Courier [10], did not rank well in the Arabic websites. However, Arial emerged as one of the top six font types used by the Arabic websites. Previous research confirmed that font type Arial was read significantly faster and was perceived as legible [10]. Design guidelines have indicated that font size 12 points (~ 16 pixels) is the most suited size for displaying text on English websites [39]. This is somewhat disputable as subsequent research suggested the use of font size 14 points (~19 pixels) instead. For displaying the Arabic text, recommendations are inconclusive yet. For example, [17] proposed to use font 14 points (~19 pixels) whereas [4] argued that font size 16 (22 pixels) to 18 points (~24 pixels) must be used for better readability. These suggestions are in strike contrast with the current practices of the Arabic web design. More than 60% of the inspected websites used font size ranging between 12 pixels to 16 pixels (i.e. 9 points to 12 points) to style the paragraphs. Similarly, menu items are sized from 13 pixels to 14 pixels, which is still considerably illegible [17]. In respect to using images in web design, we aimed at answering the following question. What types of images are incorporated within the Saudi websites given the Saudi culture? All Arabic websites included images as part of their content. Authors in [40] and [41] suggested that graphics improve the overall attractiveness of websites. Moreover, 90% of the Arabic websites we tested included human images. This is known to improve user engagement, trust, and satisfaction [21]. However, 80% of the Arabic websites used conservative images that respect the Islamic identity and cultural values of the Saudi people. Research studies agree that web designs should adhere to the cultural values of its users to achieve success and acceptance [42], [43], [44]. Two-thirds of the websites used images of both genders. The remaining third, however, used images of men only. This could be explained by the masculine dimension of the Saudi society as indicated by Hofstede scores [45]. More than 80% of the websites included images containing groups of people. Again, this can be justified by the collectivism dimension of the Saudi society [45]. Finally, there was high usage of animations, possibly, in an attempt to engage web visitors and improve the aesthetics of the websites. Evidently, the high presence of images in these websites contributed to lower performance scores and increased site loading time. Optimization of images‟ size, using the appropriate image compression techniques, is therefore recommended as a result of our analysis. Authors:
(1) Abdallah Namoun, Department of Information Systems, Faculty of Computer and Information Systems, Madinah, Saudi Arabia;
(2) Ahmad B. Alkhodre, Department of Information Technology, Faculty of Computer and Information Systems, Madinah, Saudi Arabia. This paper is available on arxiv under CC BY 4.0 DEED license. This is Part 6 of a 7-part series of the research paper “Towards Usability Guidelines for the Design of Effective Arabic Websites”. Use the table of links below to navigate to the other parts. This is Part 6 of a 7-part series of the research paper “ Towards Usability Guidelines for the Design of Effective Arabic Websites ”. Use the table of links below to navigate to the other parts. Part 6 Towards Usability Guidelines for the Design of Effective Arabic Websites Table of Links Abstract and I. Introduction Abstract and I. Introduction II. Previous Works II. Previous Works III. Research Methodology III. Research Methodology IV. Font and Image Inspection Studies IV. Font and Image Inspection Studies V. Results V. Results VI. Discussion VI. Discussion VII. Conclusions, Future Research Directions, and References VII. Conclusions, Future Research Directions, and References VI. DISCUSSION Our comprehensive inspection of current practices concerning text formatting and image usage within the top visited Arabic websites in Saudi Arabia revealed various interesting findings. The usability inspection was performed to gather insights about the font types and sizes used to style Arabic text, especially that they could directly influence the legibility of text on websites. Let us review and attempt to answer the research questions posited in the introduction. What font types and font sizes are used by major Arabic websites? On the positive side, the selection of the Arabic websites included a large pool of websites, which were selected objectively by relying on Alexa Internet latest ranking. In effect, the inspection covered a total of 73 top viewed websites (52 local and 21 international) in Saudi Arabia. The websites' ranking is based on a set of metrics, primarily the average viewing time for the last three months. Typically, a font has several characteristics including type, size, width, weight, and serifs [37], [46]. However, for the purpose of this research, we directed our focus towards two key font characteristics namely type and size. On the web, font type usually refers to the font family that represents a certain typeface, including all sizes and styles, for example, Arial and Verdana. To style a particular family type, the size of text may be increased or decreased using the font size attribute. There are different ways to resize the font including Ems (em), pixels (px), points (pt), and percent (%). In our font size analysis, we used pixels (px) as the sole measurement for the font since it is the main measurement unit for media shown on computer screens. Moreover, web designers usually use pixels as their key measurement unit for font size. Points, however, are used to measure font size for print media. It is noted that more than half of the Arabic websites breached the principle of consistency when applying font types to the text. This means that multiple font types were used on the same web pages. Previous research, however, has already emphasized the role of consistency of user interface elements, such as font, in the overall usability of websites [35], [36]. On that basis, it is recommended that designers should adhere to the same font family to create attractive and consistent Arabic web designs. Moreover, there was no evident consensus amongst the websites in favoring a particular font type in order to display the Arabic text. More than 35 font types were used by the selected 73 websites. There are various potential theories that could explain this staggering variability; firstly, the lack of research and thereby guidelines with respect to styling Arabic text to guide the effective design of Arabic websites; secondly, the weak conformance to international design practices and recommendations; thirdly, the lack of awareness that text formatting might ultimately impact text legibility and thereby readers' mental load and overall satisfaction. Nonetheless, a pattern of font usage emerged within the Arabic websites; six font types recurred several times in the formatting of titles/headline, menus, and paragraphs. These font types were used differently according to the type of text element. For titles and menus, Droid Arabic Kufi, Tahoma, Helvetica, and Arial, emerged as favorites. It is no surprise that Droid Arabic Kufi came out as a winner for it is a unique font that reflects the Arabic calligraphy. This font gives a true feeling of the traditional Arabic scripts (Kufic scripts) that date back to the 7th century. For paragraphs, Tahoma, Helvetica, Arial and Times New Roman were used more frequently. International recommendations suggest using font type Verdana since it is one of the most legible fonts as rated by online readers of English websites [38]. Nonetheless, this font did not appear frequently in the Arabic websites that we tested. Moreover, other famous fonts that were found earlier to be legible or attractive by English readers, such as Georgia [18] and Courier [10], did not rank well in the Arabic websites. However, Arial emerged as one of the top six font types used by the Arabic websites. Previous research confirmed that font type Arial was read significantly faster and was perceived as legible [10]. Design guidelines have indicated that font size 12 points (~ 16 pixels) is the most suited size for displaying text on English websites [39]. This is somewhat disputable as subsequent research suggested the use of font size 14 points (~19 pixels) instead. For displaying the Arabic text, recommendations are inconclusive yet. For example, [17] proposed to use font 14 points (~19 pixels) whereas [4] argued that font size 16 (22 pixels) to 18 points (~24 pixels) must be used for better readability. These suggestions are in strike contrast with the current practices of the Arabic web design. More than 60% of the inspected websites used font size ranging between 12 pixels to 16 pixels (i.e. 9 points to 12 points) to style the paragraphs. Similarly, menu items are sized from 13 pixels to 14 pixels, which is still considerably illegible [17]. In respect to using images in web design, we aimed at answering the following question. What types of images are incorporated within the Saudi websites given the Saudi culture? All Arabic websites included images as part of their content. Authors in [40] and [41] suggested that graphics improve the overall attractiveness of websites. Moreover, 90% of the Arabic websites we tested included human images. This is known to improve user engagement, trust, and satisfaction [21]. However, 80% of the Arabic websites used conservative images that respect the Islamic identity and cultural values of the Saudi people. Research studies agree that web designs should adhere to the cultural values of its users to achieve success and acceptance [42], [43], [44]. Two-thirds of the websites used images of both genders. The remaining third, however, used images of men only. This could be explained by the masculine dimension of the Saudi society as indicated by Hofstede scores [45]. More than 80% of the websites included images containing groups of people. Again, this can be justified by the collectivism dimension of the Saudi society [45]. Finally, there was high usage of animations, possibly, in an attempt to engage web visitors and improve the aesthetics of the websites. Evidently, the high presence of images in these websites contributed to lower performance scores and increased site loading time. Optimization of images‟ size, using the appropriate image compression techniques, is therefore recommended as a result of our analysis. Authors: (1) Abdallah Namoun, Department of Information Systems, Faculty of Computer and Information Systems, Madinah, Saudi Arabia; (2) Ahmad B. Alkhodre, Department of Information Technology, Faculty of Computer and Information Systems, Madinah, Saudi Arabia. Authors : Authors (1) Abdallah Namoun, Department of Information Systems, Faculty of Computer and Information Systems, Madinah, Saudi Arabia; (2) Ahmad B. Alkhodre, Department of Information Technology, Faculty of Computer and Information Systems, Madinah, Saudi Arabia. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

Design Arabic Websites with Consistent Fonts, Optimal Sizes, and Culturally Aligned Images

Authors:
(1) Jongmin Lee, Department of Mathematical Science, Seoul National University;
(2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction 1.1 Notations and preliminaries 1.2 Prior works 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 4 Complexity lower bound 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries B Omitted proofs in Section 2 C Omitted proofs in Section 3 D Omitted proofs in Section 4 E Omitted proofs in Section 5 F Omitted proofs in Section 6 G Broader Impacts H Limitations 2.2 Accelerated rate for Bellman optimality opera We now present the accelerated convergence rate of Anc-VI for the Bellman optimality operator. Our analysis uses what we call the Bellman anti-optimality operator, define Anc-VI with the Bellman optimality operator exhibits the same accelerated convergence rate as Anc-VI with the Bellman consistency operator. As in Theorem 1, the rate of Theorem 2 also becomes O(1/k) when γ ≈ 1, while VI has a O(1)-rate. Proof outline of Theorem 2. The key technical challenge of the proof comes from the fact that the Bellman optimality operator is non-linear. Similar to the Bellman consistency operator case, we have This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Authors: Authors: (1) Jongmin Lee, Department of Mathematical Science, Seoul National University; (2) Ernest K. Ryu, Department of Mathematical Science, Seoul National University and Interdisciplinary Program in Artificial Intelligence, Seoul National University. Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Notations and preliminaries 1.1 Notations and preliminaries 1.2 Prior works 1.2 Prior works 2 Anchored Value Iteration 2 Anchored Value Iteration 2.1 Accelerated rate for Bellman consistency operator 2.1 Accelerated rate for Bellman consistency operator 2.2 Accelerated rate for Bellman optimality opera 2.2 Accelerated rate for Bellman optimality opera 3 Convergence when y=1 3 Convergence when y=1 4 Complexity lower bound 4 Complexity lower bound 5 Approximate Anchored Value Iteration 5 Approximate Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 6 Gauss–Seidel Anchored Value Iteration 7 Conclusion, Acknowledgments and Disclosure of Funding and References 7 Conclusion, Acknowledgments and Disclosure of Funding and References A Preliminaries A Preliminaries B Omitted proofs in Section 2 B Omitted proofs in Section 2 C Omitted proofs in Section 3 C Omitted proofs in Section 3 D Omitted proofs in Section 4 D Omitted proofs in Section 4 E Omitted proofs in Section 5 E Omitted proofs in Section 5 F Omitted proofs in Section 6 F Omitted proofs in Section 6 G Broader Impacts G Broader Impacts H Limitations H Limitations 2.2 Accelerated rate for Bellman optimality opera We now present the accelerated convergence rate of Anc-VI for the Bellman optimality operator. Our analysis uses what we call the Bellman anti-optimality operator, define Anc-VI with the Bellman optimality operator exhibits the same accelerated convergence rate as Anc-VI with the Bellman consistency operator. As in Theorem 1, the rate of Theorem 2 also becomes O(1/k) when γ ≈ 1, while VI has a O(1)-rate. Proof outline of Theorem 2. The key technical challenge of the proof comes from the fact that the Bellman optimality operator is non-linear. Similar to the Bellman consistency operator case, we have This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

How Anc-VI Helps AI Learn Faster with Optimality Operators

Table of Links Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 3. Methodology 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 6. Conclusions Appendix and References 5.6. Comparison of ClassBD filters Given that ClassBD comprises two filters, we explore their respective contributions in this experiment. Here we test four combinations: a standalone time domain filter (T-filter), a standalone frequency domain filter (F-filter), an F-filter followed by a T-filter, and our proposed scheme (a T-filter followed by an F-filter). The results are presented in Table 15. Primarily, our scheme exhibits superior performance, indicating that both filters contribute significantly to the classification. Secondly, when comparing the single T-filter and F-filter, their performances are found to be dataset-dependent. On the PU and HIT datasets, T-filters outperform F-filters, whereas their performance is inferior to F-filters on the JNU dataset. Authors:
(1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China;
(3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China;
(4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 2.2. Quadratic neural networks 3. Methodology 3. Methodology 3.1. Time domain quadratic convolutional filter 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 5.6. Comparison of ClassBD filters 6. Conclusions 6. Conclusions Appendix and References Appendix and References 5.6. Comparison of ClassBD filters Given that ClassBD comprises two filters, we explore their respective contributions in this experiment. Here we test four combinations: a standalone time domain filter (T-filter), a standalone frequency domain filter (F-filter), an F-filter followed by a T-filter, and our proposed scheme (a T-filter followed by an F-filter). The results are presented in Table 15. Primarily, our scheme exhibits superior performance, indicating that both filters contribute significantly to the classification. Secondly, when comparing the single T-filter and F-filter, their performances are found to be dataset-dependent. On the PU and HIT datasets, T-filters outperform F-filters, whereas their performance is inferior to F-filters on the JNU dataset. Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. Authors: Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv

Researchers Discover Optimal Combination of Time and Frequency Domain Filters in ClassBD

Authors:
(1) Xian Liu, Snap Inc., CUHK with Work done during an internship at Snap Inc.;
(2) Jian Ren, Snap Inc. with Corresponding author: jren@snapchat.com;
(3) Aliaksandr Siarohin, Snap Inc.;
(4) Ivan Skorokhodov, Snap Inc.;
(5) Yanyu Li, Snap Inc.;
(6) Dahua Lin, CUHK;
(7) Xihui Liu, HKU;
(8) Ziwei Liu, NTU;
(9) Sergey Tulyakov, Snap Inc. Table of Links Abstract and 1 Introduction 2 Related Work 3 Our Approach and 3.1 Preliminaries and Problem Setting 3.2 Latent Structural Diffusion Model 3.3 Structure-Guided Refiner 4 Human Verse Dataset 5 Experiments 5.1 Main Results 5.2 Ablation Study 6 Discussion and References A Appendix and A.1 Additional Quantitative Results A.2 More Implementation Details and A.3 More Ablation Study Results A.4 More User Study Details A.5 Impact of Random Seed and Model Robustness and A.6 Boarder Impact and Ethical Consideration A.7 More Comparison Results and A.8 Additional Qualitative Results A.9 Licenses 5.2 ABLATION STUDY Simultaneous Denoise with Expert Branch. We explore whether latent structural diffusion model helps, and how many layers to replicate in the structural expert branches: 1) Denoise RGB, that only learns to denoise an image. 2) Denoise RGB + Depth, which also predicts depth. 3) Half DownBlock & UpBlock. We replicate half of the first DownBlock and the last UpBlock, which contains one down/up-sample ResBlock and one AttnBlock. 4) Two DownBlocks & UpBlocks, where we copy the first two DownBlocks and the last two UpBlocks. The results are shown in Tab. 2 (top), which prove that the joint learning of image appearance, spatial relationship, and geometry is beneficial. We also find that while fewer replicate layers give more spatially aligned results, the per-branch parameters are insufficient to capture distributions of each modality. In contrast, excessive replicate layers lead to less feature fusion across different targets, which fails to complement to each other branches. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Xian Liu, Snap Inc., CUHK with Work done during an internship at Snap Inc.; (2) Jian Ren, Snap Inc. with Corresponding author: jren@snapchat.com; (3) Aliaksandr Siarohin, Snap Inc.; (4) Ivan Skorokhodov, Snap Inc.; (5) Yanyu Li, Snap Inc.; (6) Dahua Lin, CUHK; (7) Xihui Liu, HKU; (8) Ziwei Liu, NTU; (9) Sergey Tulyakov, Snap Inc. Authors: Authors: (1) Xian Liu, Snap Inc., CUHK with Work done during an internship at Snap Inc.; (2) Jian Ren, Snap Inc. with Corresponding author: jren@snapchat.com; (3) Aliaksandr Siarohin, Snap Inc.; (4) Ivan Skorokhodov, Snap Inc.; (5) Yanyu Li, Snap Inc.; (6) Dahua Lin, CUHK; (7) Xihui Liu, HKU; (8) Ziwei Liu, NTU; (9) Sergey Tulyakov, Snap Inc. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Work 2 Related Work 3 Our Approach and 3.1 Preliminaries and Problem Setting 3 Our Approach and 3.1 Preliminaries and Problem Setting 3.2 Latent Structural Diffusion Model 3.2 Latent Structural Diffusion Model 3.3 Structure-Guided Refiner 3.3 Structure-Guided Refiner 4 Human Verse Dataset 4 Human Verse Dataset 5 Experiments 5 Experiments 5.1 Main Results 5.1 Main Results 5.2 Ablation Study 5.2 Ablation Study 6 Discussion and References 6 Discussion and References A Appendix and A.1 Additional Quantitative Results A Appendix and A.1 Additional Quantitative Results A.2 More Implementation Details and A.3 More Ablation Study Results A.2 More Implementation Details and A.3 More Ablation Study Results A.4 More User Study Details A.4 More User Study Details A.5 Impact of Random Seed and Model Robustness and A.6 Boarder Impact and Ethical Consideration A.5 Impact of Random Seed and Model Robustness and A.6 Boarder Impact and Ethical Consideration A.7 More Comparison Results and A.8 Additional Qualitative Results A.7 More Comparison Results and A.8 Additional Qualitative Results A.9 Licenses A.9 Licenses 5.2 ABLATION STUDY Simultaneous Denoise with Expert Branch. We explore whether latent structural diffusion model helps, and how many layers to replicate in the structural expert branches: 1) Denoise RGB, that only learns to denoise an image. 2) Denoise RGB + Depth, which also predicts depth. 3) Half DownBlock & UpBlock. We replicate half of the first DownBlock and the last UpBlock, which contains one down/up-sample ResBlock and one AttnBlock. 4) Two DownBlocks & UpBlocks, where we copy the first two DownBlocks and the last two UpBlocks. The results are shown in Tab. 2 (top), which prove that the joint learning of image appearance, spatial relationship, and geometry is beneficial. We also find that while fewer replicate layers give more spatially aligned results, the per-branch parameters are insufficient to capture distributions of each modality. In contrast, excessive replicate layers lead to less feature fusion across different targets, which fails to complement to each other branches. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

HyperHuman Ablation Study: Optimal Expert Branch Design for Improved Image Generation

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3.5 Comparison with classical Bayesian persuasion strategies Given the optimal signaling strategy derived in Lemma 5, one natural followup question is the quantification of the sender’s utility improvement obtained by adopting the optimal signaling strategy in comparison to using strategies structurally similar to the optimal strategies in classical Bayesian persuasion for a binary state of the world. Owing the page limit, we directly define a class of strategies structurally similar to the classical Bayesian persuasion strategy below and provide the justification in our online version [23]. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3.5 Comparison with classical Bayesian persuasion strategies Given the optimal signaling strategy derived in Lemma 5, one natural followup question is the quantification of the sender’s utility improvement obtained by adopting the optimal signaling strategy in comparison to using strategies structurally similar to the optimal strategies in classical Bayesian persuasion for a binary state of the world. Owing the page limit, we directly define a class of strategies structurally similar to the classical Bayesian persuasion strategy below and provide the justification in our online version [23]. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. Definition 4. With binary states of the world, a (binary-state) Bayesian persuasion (BBP) strategy is a strategy that “mixes two possible states in one signal and reveals the true state on the other signal”. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

How Optimal Signaling Outperforms Classical Bayesian Strategies in Multi-Phase Trials

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 3 Binary-outcome Experiments in Two-phase Trials In this section the sender’s optimization problem presented in (2) Section 2.1, is solved starting with the simplest non-trivial case. There are only two phases in the trial studied here, and from this we will develop more insight into how different types of experiments (determined versus sender-designed) influence the optimal signaling strategy of the sender. To be more specific, we will analyze how two determined experiments (in phase II) and one sender-designed experiment (in phase I) will impact the sender’s optimal signaling strategy. Before we present the general case, we discuss a subset class of two-phase trials that are similar to single-phase trials. In this class of two-phase trials, in one of the phase-II experiments, called a trivial experiment, the outcome distribution is independent of the true state. Trivial experiments [2], also called (Blackwell) non-informative experiments in some literature, are frequently used as benchmarks to compare the agents’ expected utility change under different signaling schemes/mechanisms, e.g., [22,20,21]. This two-phase model with a trivial experiment tries to capture real-world problems with one actual (and costly) experiment, e.g., clinical trials, venture capital investments, or space missions. Since the experiment is costly, a screening procedure is provided to decide whether it is worth conducting the experiment. We will then analyze the optimal signaling strategy in the general scenario, where both experiments in phase II are non-trivial. 3.1 Experiments with screenings We start by analyzing the sender’s optimal strategy (signaling structure) in a simple scenario where there is one non-trivial experiment conducted in phase II. The sender’s authority on choosing the probability pair (p1, p2) controls the screening process. To avoid any ambiguity, we first define what a trivial experiment is. When a trivial experiment (in phase II) is conducted, the posterior belief of the state stays the same as the interim belief derived in (1). When there exists a trivial experiment in the two phase-II trial options, then Lemma 1 states that the sender and the receiver’s expected utility under the optimal signaling strategy is the same as in the (single-phase) classical Bayesian persuasion problem. Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Bayesian persuasion in a single-phase trial,


Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. In the single-trial classical Bayesian persuasion setting, the optimal signaling strategy only mixes the two possible states in one outcome (e.g., when the prosecutor claims the suspect is guilty). On the other outcome, the sender reveals the true state with probability one (e.g., when the prosecutor says the suspect is innocent). When there is a trivial experiment in phase II, the other experiment (supposing that it will be conducted at outcome ωB) will be rendered defunct by the sender’s choice of experiments in phase I. This phenomenon occurs because the sender can always choose to reveal the true state when the non-trivial experiment is to be conducted, i.e., by setting P(θ1|EB) = 1 or P(θ2|EB) = 1; and the classical Bayesian persuasion strategy can be replicated. In essence, having a trivial experiment in the phase-II trial does not constrain the sender. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 3 Binary-outcome Experiments in Two-phase Trials In this section the sender’s optimization problem presented in (2) Section 2.1, is solved starting with the simplest non-trivial case. There are only two phases in the trial studied here, and from this we will develop more insight into how different types of experiments (determined versus sender-designed) influence the optimal signaling strategy of the sender. To be more specific, we will analyze how two determined experiments (in phase II) and one sender-designed experiment (in phase I) will impact the sender’s optimal signaling strategy. Before we present the general case, we discuss a subset class of two-phase trials that are similar to single-phase trials. In this class of two-phase trials, in one of the phase-II experiments, called a trivial experiment, the outcome distribution is independent of the true state. Trivial experiments [2], also called (Blackwell) non-informative experiments in some literature, are frequently used as benchmarks to compare the agents’ expected utility change under different signaling schemes/mechanisms, e.g., [22,20,21]. This two-phase model with a trivial experiment tries to capture real-world problems with one actual (and costly) experiment, e.g., clinical trials, venture capital investments, or space missions. Since the experiment is costly, a screening procedure is provided to decide whether it is worth conducting the experiment. We will then analyze the optimal signaling strategy in the general scenario, where both experiments in phase II are non-trivial. 3.1 Experiments with screenings We start by analyzing the sender’s optimal strategy (signaling structure) in a simple scenario where there is one non-trivial experiment conducted in phase II. The sender’s authority on choosing the probability pair (p1, p2) controls the screening process. To avoid any ambiguity, we first define what a trivial experiment is. When a trivial experiment (in phase II) is conducted, the posterior belief of the state stays the same as the interim belief derived in (1). When there exists a trivial experiment in the two phase-II trial options, then Lemma 1 states that the sender and the receiver’s expected utility under the optimal signaling strategy is the same as in the (single-phase) classical Bayesian persuasion problem. Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Lemma 1. When the state space is binary, both sender and receiver’s expected utilities are the same in the following two Bayesian persuasion schemes under each scheme’s optimal signaling strategy: Bayesian persuasion in a single-phase trial, Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a single-phase trial, Bayesian persuasion in a single-phase trial, Bayesian persuasion in a single-phase trial, Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. Bayesian persuasion in a two-phase trial with a sender-designed phase-I experiment and a trivial experiment in phase II. In the single-trial classical Bayesian persuasion setting, the optimal signaling strategy only mixes the two possible states in one outcome (e.g., when the prosecutor claims the suspect is guilty). On the other outcome, the sender reveals the true state with probability one (e.g., when the prosecutor says the suspect is innocent). When there is a trivial experiment in phase II, the other experiment (supposing that it will be conducted at outcome ωB) will be rendered defunct by the sender’s choice of experiments in phase I. This phenomenon occurs because the sender can always choose to reveal the true state when the non-trivial experiment is to be conducted, i.e., by setting P(θ1|EB) = 1 or P(θ2|EB) = 1; and the classical Bayesian persuasion strategy can be replicated. In essence, having a trivial experiment in the phase-II trial does not constrain the sender. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Analyzing Optimal Signaling with Binary-outcome Experiments in Two-phase Trials

Ontleed optimale sein met binêre uitkoms-eksperimente in twee-fase proewe

Análisis de la señalización óptima con experimentos de resultados binarios en ensayos de dos fases

تجزیه و تحلیل سیگنال دهی بهینه با آزمایش های باینری نتیجه در آزمایشات دو فازی

Analiza optimalnog signaliziranja s eksperimentima s binarnim ishodom u dvofaznim ispitivanjima

2段階試験におけるバイナリ結果実験による最適なシグナル伝達の分析

ოპტიმალური სიგნალიზაციის ანალიზი ორფაზიან ცდებში ორფაზიანი ექსპერიმენტებით

Екі фазалық сынақтардағы екілік нәтиже эксперименттерімен оңтайлы сигналды талдау

Go sekaseka Matshwao a Mabotse ka Diteko tša dipoelo tša Binary ka Ditekong tša Megato ye Mebedi

Анализ оптимальной сигнализации с помощью экспериментов с бинарным результатом в двухфазных испытаниях

Gusesengura Ibimenyetso Byiza hamwe na Binary-ibisubizo Ubushakashatsi Mubice bibiri

Анализа оптималне сигнализације са експериментима са бинарним исходом у двофазним испитивањима

دو فیز ٹرائلز میں بائنری نتائج کے تجربات کے ساتھ بہترین سگنلنگ کا تجزیہ کرنا

Authors:
(1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu);
(2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu);
(3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 2 Problem Formulation Before the receiver takes his action, a trial consisting of multiple phases will be run, and the outcome in each phase will be revealed to him. In each phase, one experiment will be conducted, which is chosen according to the outcomes in earlier phases. Hence, the experiment outcomes in earlier phases not only affect the interim belief but also influence the possible (sequence of) experiments that will be conducted afterward. In the most sender-friendly setup where the sender can choose any experiment in each phase without any constraints, the problem is equivalent to the classical Bayesian persuasion problem with an enlarged signal space. However, when some experiments are pre-determined conditional on a set of outcomes, the sender must take these constraints into account to design her optimal signaling structure. To present our results on the influence of multiple phases on the sender’s signaling strategy, we start with a model of two-phase trials with binary-outcome experiments in the rest of this section. We then analyze the optimal signaling strategy of this model in Section 3. After that, we will introduce the general model of multiple-phase trials with binary-outcome experiments and propose a systematic approach to analyze the optimal signaling structure in Section 4. This paper is available on arxiv under CC 4.0 license. Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Authors: Authors: (1) Shih-Tang Su, University of Michigan, Ann Arbor (shihtang@umich.edu); (2) Vijay G. Subramanian, University of Michigan, Ann Arbor and (vgsubram@umich.edu); (3) Grant Schoenebeck, University of Michigan, Ann Arbor (schoeneb@umich.edu). Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Problem Formulation 2. Problem Formulation 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 2.1 Model of Binary-Outcome Experiments in Two-Phase Trials 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3 Binary-outcome Experiments in Two-phase Trials and 3.1 Experiments with screenings 3.2 Assumptions and induced strategies 3.2 Assumptions and induced strategies 3.3 Constraints given by phase-II experiments 3.3 Constraints given by phase-II experiments 3.4 Persuasion ratio and the optimal signaling structure 3.4 Persuasion ratio and the optimal signaling structure 3.5 Comparison with classical Bayesian persuasion strategies 3.5 Comparison with classical Bayesian persuasion strategies 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4 Binary-outcome Experiments in Multi-phase trials and 4.1 Model of binary-outcome experiments in multi-phase trials 4.2 Determined versus sender-designed experiments 4.2 Determined versus sender-designed experiments 4.3 Multi-phase model and classical Bayesian persuasion and References 4.3 Multi-phase model and classical Bayesian persuasion and References 2 Problem Formulation Before the receiver takes his action, a trial consisting of multiple phases will be run, and the outcome in each phase will be revealed to him. In each phase, one experiment will be conducted, which is chosen according to the outcomes in earlier phases. Hence, the experiment outcomes in earlier phases not only affect the interim belief but also influence the possible (sequence of) experiments that will be conducted afterward. In the most sender-friendly setup where the sender can choose any experiment in each phase without any constraints, the problem is equivalent to the classical Bayesian persuasion problem with an enlarged signal space. However, when some experiments are pre-determined conditional on a set of outcomes, the sender must take these constraints into account to design her optimal signaling structure. To present our results on the influence of multiple phases on the sender’s signaling strategy, we start with a model of two-phase trials with binary-outcome experiments in the rest of this section. We then analyze the optimal signaling strategy of this model in Section 3. After that, we will introduce the general model of multiple-phase trials with binary-outcome experiments and propose a systematic approach to analyze the optimal signaling structure in Section 4. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

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