Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

At the dawn of the fourth industrial revolution, we are witnessing a fast and widespread adoption of artificial intelligence (AI) in our daily life, which contributes to accelerating the shift towards a more algorithmic society. However, even with such unprecedented advancements, a key impediment to the use of AI-based systems is that they often lack transparency. Indeed, the black-box nature of these systems allows powerful predictions, but it cannot be directly explained. This issue has triggered a new debate on explainable AI (XAI). A research field holds substantial promise for improving trust and transparency of AI-based systems. It is recognized as the sine qua non for AI to continue making steady progress without disruption. This survey provides an entry point for interested researchers and practitioners to learn key aspects of the young and rapidly growing body of research related to XAI. Through the lens of the literature, we review the existing approaches regarding the topic, discuss trends surrounding its sphere, and present major research trajectories.

Peeking Inside the Black-Box: A Survey on Explainable Artificial Intelligence (XAI)

Machine learning systems are becoming increasingly ubiquitous. These systems’s adoption has been expanding, accelerating the shift towards a more algorithmic society, meaning that algorithmically informed decisions have greater potential for significant social impact. However, most of these accurate decision support systems remain complex black boxes, meaning their internal logic and inner workings are hidden to the user and even experts cannot fully understand the rationale behind their predictions. Moreover, new regulations and highly regulated domains have made the audit and verifiability of decisions mandatory, increasing the demand for the ability to question, understand, and trust machine learning systems, for which interpretability is indispensable. The research community has recognized this interpretability problem and focused on developing both interpretable models and explanation methods over the past few years. However, the emergence of these methods shows there is no consensus on how to assess the explanation quality. Which are the most suitable metrics to assess the quality of an explanation? The aim of this article is to provide a review of the current state of the research field on machine learning interpretability while focusing on the societal impact and on the developed methods and metrics. Furthermore, a complete literature review is presented in order to identify future directions of work on this field.

Machine Learning Interpretability: A Survey on Methods and Metrics

Increasingly, organizations are pairing humans with AI systems to improve decision-making and reducing costs Proponents of human-centered AI argue that team performance can even further improve when the AI model explains its recommendations However, a careful analysis of existing literature reveals that prior studies observed improvements due to explanations only when the AI, alone, outperformed both the human and the best human-AI team This raises an important question: can explanations lead to complementary performance, ie, with accuracy higher than both the human and the AI working alone? 
We address this question by devising comprehensive studies on human-AI teaming, where participants solve a task with help from an AI system without explanations and from one with varying types of AI explanation support We carefully controlled to ensure comparable human and AI accuracy across experiments on three NLP datasets (two for sentiment analysis and one for question answering) While we found complementary improvements from AI augmentation, they were not increased by state-of-the-art explanations compared to simpler strategies, such as displaying the AI's confidence We show that explanations increase the chance that humans will accept the AI's recommendation regardless of whether the AI is correct While this clarifies the gains in team performance from explanations in prior work, it poses new challenges for human-centered AI: how can we best design systems to produce complementary performance? Can we develop explanatory approaches that help humans decide whether and when to trust AI input?

Does the Whole Exceed its Parts? The Effect of AI Explanations on Complementary Team Performance

We provide a new analysis of local SGD, removing unnecessary assumptions and elaborating on the difference between two data regimes: identical and heterogeneous. In both cases, we improve the existing theory and provide values of the optimal stepsize and optimal number of local iterations. Our bounds are based on a new notion of variance that is specific to local SGD methods with different data. The tightness of our results is guaranteed by recovering known statements when we plug $H=1$, where $H$ is the number of local steps. The empirical evidence further validates the severe impact of data heterogeneity on the performance of local SGD.

Tighter Theory for Local SGD on Identical and Heterogeneous Data.

As artificial intelligence is increasingly affecting all parts of society and life, there is growing recognition that human interpretability of machine learning models is important. It is often argued that accuracy or other similar generalization performance metrics must be sacrificed in order to gain interpretability. Such arguments, however, fail to acknowledge that the overall decision-making system is composed of two entities: the learned model and a human who fuses together model outputs with his or her own information. As such, the relevant performance criteria should be for the entire system, not just for the machine learning component. In this work, we characterize the performance of such two-node tandem data fusion systems using the theory of distributed detection. In doing so, we work in the population setting and model interpretable learned models as multi-level quantizers. We prove that under our abstraction, the overall system of a human with an interpretable classifier outperforms one with a black box classifier.

Why Interpretability in Machine Learning? An Answer Using Distributed Detection and Data Fusion Theory.

In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex functions. The objective and constraint functions are revealed locally to the nodes, at each time, after taking an action. Naturally, the constraints cannot be instantaneously satisfied. Therefore, we reformulate the problem to satisfy these constraints in the long term. To this end, we propose a distributed primal-dual mirror descent based approach, in which the primal and dual updates are carried out locally at all the nodes. This is followed by sharing and mixing of the primal variables by the local nodes via communication with the immediate neighbors. To quantify the performance of the proposed algorithm, we utilize the challenging, but more realistic metrics of dynamic regret and fit. Dynamic regret measures the cumulative loss incurred by the algorithm, compared to the best dynamic strategy. On the other hand, fit measures the long term cumulative constraint violations. Without assuming the restrictive Slater's conditions, we show that the proposed algorithm achieves sublinear regret and fit under mild, commonly used assumptions.

On Distributed Online Convex Optimization with Sublinear Dynamic Regret and Fit

In this paper, we consider the problem of distributed sequential detection using wireless sensor networks in the presence of imperfect communication channels between the sensors and the fusion center. Sensor observations are assumed to be spatially dependent. Moreover, the channel noise can be dependent and non-Gaussian. We propose a copula-based distributed sequential detection scheme that takes the spatial dependence into account. More specifically, each local sensor runs a memory-less truncated sequential test repeatedly and sends its binary decisions to the fusion center synchronously. The fusion center fuses the received messages using a copula-based sequential test. To this end, we first propose a centralized copula-based sequential test and show its asymptotic optimality and time efficiency. We then show the asymptotic optimality and time efficiency of the proposed distributed scheme. We also show that by suitably designing the local thresholds and the truncation window, the local probabilities of false alarm and miss detection of the proposed memory-less truncated local sequential tests satisfy the pre-specified error probabilities. Numerical experiments are conducted to demonstrate the effectiveness of our approach.

Distributed Sequential Detection: Dependent Observations and Imperfect Communication

In this paper, we propose a distributed algorithm for stochastic smooth, non-convex optimization. We assume a worker-server architecture where $N$ nodes, each having $n$ (potentially infinite) number of samples, collaborate with the help of a central server to perform the optimization task. The global objective is to minimize the average of local cost functions available at individual nodes. The proposed approach is a non-trivial extension of the popular parallel-restarted SGD algorithm, incorporating the optimal variance-reduction based SPIDER gradient estimator into it. We prove convergence of our algorithm to a first-order stationary solution. The proposed approach achieves the best known communication complexity $O(\epsilon^{-1})$ along with the optimal computation complexity. For finite-sum problems (finite $n$), we achieve the optimal computation (IFO) complexity $O(\sqrt{Nn}\epsilon^{-1})$. For online problems ($n$ unknown or infinite), we achieve the optimal IFO complexity $O(\epsilon^{-3/2})$. In both the cases, we maintain the linear speedup achieved by existing methods. This is a massive improvement over the $O(\epsilon^{-2})$ IFO complexity of the existing approaches. Additionally, our algorithm is general enough to allow non-identical distributions of data across workers, as in the recently proposed federated learning paradigm.

Parallel Restarted SPIDER - Communication Efficient Distributed Nonconvex Optimization with Optimal Computation Complexity.

In this work, we propose a non-parametric sequential hypothesis test based on random distortion testing (RDT). RDT addresses the problem of testing whether or not a random signal, $\Xi$ , observed in independent and identically distributed (i.i.d) additive noise deviates by more than a specified tolerance, $\tau$ , from a fixed model, $\xi _0$ . The test is non-parametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. The need to control the probabilities of false alarm (PFA) and missed detection (PMD), while reducing the number of samples required to make a decision, leads to a novel sequential algorithm, Seq RDT. We show that under mild assumptions on the signal, Seq RDT follows the properties desired by a sequential test. We introduce the concept of a buffer and derive bounds on PFA and PMD, from which we choose the buffer size. Simulations show that Seq RDT leads to faster decision-making on an average compared to its fixed-sample-size (FSS) counterpart, Block RDT. These simulations also show that the proposed algorithm is robust to model mismatches compared to the sequential probability ratio test (SPRT).

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Prashant Khanduri

Papers

Why Interpretability in Machine Learning? An Answer Using Distributed Detection and Data Fusion Theory.

On Distributed Online Convex Optimization with Sublinear Dynamic Regret and Fit

Distributed Sequential Detection: Dependent Observations and Imperfect Communication

Parallel Restarted SPIDER - Communication Efficient Distributed Nonconvex Optimization with Optimal Computation Complexity.

On Sequential Random Distortion Testing of Non-Stationary Processes