SEQUENTIAL METHODS FOR NON-PARAMETRIC HYPOTHESIS TESTING

In today’s world, many applications are characterized by the availability of large amounts of complex-structured data. It is not always possible to fit the data to predefined models or distributions. Model dependent signal processing approaches are often susceptible to mismatches between the data and the assumed model. In cases where the data does not conform to the assumed model, providing sufficient performance guarantees becomes a challenging task. Therefore, it is important to devise methods that are model-independent, robust, provide sufficient performance guarantees for the task at hand and, at the same time, are simple to implement. The goal of this dissertation is to develop such algorithms for two-sided sequential binary hypothesis testing. In this dissertation, we propose two algorithms for sequential non-parametric hypothesis testing. The proposed algorithms are based on the random distortion testing (RDT) framework. The RDT framework addresses the problem of testing whether a random signal observed in additive noise deviates by more than a specified tolerance from a fixed model. The data-based approach is non-parametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. Importantly, we show that the proposed algorithms are not only robust but also provide performance guarantees in the non-asymptotic regimes in contrast to the popular non-parametric likelihood ratio based approaches which provide only asymptotic performance guarantees. In the first part of the dissertation, we develop a sequential algorithm SeqRDT. We first introduce a few mild assumptions required to control the error probabilities of the algorithm. We then analyze the asymptotic properties of the algorithm along with the behavior of the thresholds. Finally, we derive the upper bounds on the probabilities of false alarm (PFA) and missed detection (PMD) and demonstrate how to choose the algorithm parameters such that PFA and PMD can be guaranteed to stay below pre-specified levels. Specifically, we present two ways to design the algorithm: We first introduce the notion of a buffer and show that with the help of a few mild assumptions we can choose an appropriate buffer size such that PFA and PMD can be controlled. Later, we eliminate the buffer by introducing additional parameters and show that with the choice of appropriate parameters we can still control the probabilities of error of the algorithm. In the second part of the dissertation, we propose a truncated (finite horizon) algorithm, TSeqRDT, for the two-sided binary hypothesis testing problem. We first present the optimal fixed-sample-size (FSS) test for the hypothesis testing problem and present a few important preliminary results required to design the truncated algorithm. Similar, to the non-truncated case we first analyze the properties of the thresholds and then derive the upper bounds on PFA and PMD. We then choose the thresholds such that the proposed algorithm not only guarantees the error probabilities to be below pre-specified levels but at the same time makes a decision faster on average compared to its optimal FSS counterpart. We show that the truncated algorithm requires fewer assumptions on the signal model compared to the non-truncated case. We also derive bounds on the average stopping times of the algorithm. Importantly, we study the trade-off between the stopping time and the error probabilities of the algorithm and propose a method to choose the algorithm parameters. Finally, via numerical simulations, we compare the performance of T-SeqRDT and SeqRDT to sequential probability ratio test (SPRT) and composite sequential probability ratio tests. We also show the robustness of the proposed approaches compared to the standard likelihood ratio based approaches

Distributed Sequential Hypothesis Testing with Dependent Sensor Observations

In this paper, we consider the problem of distributed sequential detection using wireless sensor networks (WSNs) in the presence of imperfect communication channels between the sensors and the fusion center (FC). We assume that sensor observations are spatially dependent. We propose a copula-based distributed sequential detection scheme that characterizes the spatial dependence. Specifically, each local sensor collects observations regarding the phenomenon of interest and forwards the information obtained to the FC over noisy channels. The FC fuses the received messages using a copula-based sequential test. Moreover, we show the asymptotic optimality of the proposed copula-based sequential test. Numerical experiments are conducted to demonstrate the effectiveness of our approach

Fairness-aware Vision Transformer via Debiased Self-Attention

Vision Transformer (ViT) has recently gained significant interest in solving computer vision (CV) problems due to its capability of extracting informative features and modeling long-range dependencies through the self-attention mechanism. To fully realize the advantages of ViT in real-world applications, recent works have explored the trustworthiness of ViT, including its robustness and explainability. However, another desiderata, fairness has not yet been adequately addressed in the literature. We establish that the existing fairness-aware algorithms (primarily designed for CNNs) do not perform well on ViT. This necessitates the need for developing our novel framework via Debiased Self-Attention (DSA). DSA is a fairness-through-blindness approach that enforces ViT to eliminate spurious features correlated with the sensitive attributes for bias mitigation. Notably, adversarial examples are leveraged to locate and mask the spurious features in the input image patches. In addition, DSA utilizes an attention weights alignment regularizer in the training objective to encourage learning informative features for target prediction. Importantly, our DSA framework leads to improved fairness guarantees over prior works on multiple prediction tasks without compromising target prediction performance

An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learning

Recently, bi-level optimization (BLO) has taken center stage in some very exciting developments in the area of signal processing (SP) and machine learning (ML). Roughly speaking, BLO is a classical optimization problem that involves two levels of hierarchy (i.e., upper and lower levels), wherein obtaining the solution to the upper-level problem requires solving the lower-level one. BLO has become popular largely because it is powerful in modeling problems in SP and ML, among others, that involve optimizing nested objective functions. Prominent applications of BLO range from resource allocation for wireless systems to adversarial machine learning. In this work, we focus on a class of tractable BLO problems that often appear in SP and ML applications. We provide an overview of some basic concepts of this class of BLO problems, such as their optimality conditions, standard algorithms (including their optimization principles and practical implementations), as well as how they can be leveraged to obtain state-of-the-art results for a number of key SP and ML applications. Further, we discuss some recent advances in BLO theory, its implications for applications, and point out some limitations of the state-of-the-art that require significant future research efforts. Overall, we hope that this article can serve to accelerate the adoption of BLO as a generic tool to model, analyze, and innovate on a wide array of emerging SP and ML applications