Showing papers in "Journal of Machine Learning Research in 2020"

Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer

Abstract: Transfer learning, where a model is first pre-trained on a data-rich task before being fine-tuned on a downstream task, has emerged as a powerful technique in natural language processing (NLP). The effectiveness of transfer learning has given rise to a diversity of approaches, methodology, and practice. In this paper, we explore the landscape of transfer learning techniques for NLP by introducing a unified framework that converts all text-based language problems into a text-to-text format. Our systematic study compares pre-training objectives, architectures, unlabeled data sets, transfer approaches, and other factors on dozens of language understanding tasks. By combining the insights from our exploration with scale and our new ``Colossal Clean Crawled Corpus'', we achieve state-of-the-art results on many benchmarks covering summarization, question answering, text classification, and more. To facilitate future work on transfer learning for NLP, we release our data set, pre-trained models, and code.

Monte Carlo Gradient Estimation in Machine Learning

Abstract: This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; the problem of sensitivity analysis. In machine learning research, this gradient problem lies at the core of many learning problems, in supervised, unsupervised and reinforcement learning. We will generally seek to rewrite such gradients in a form that allows for Monte Carlo estimation, allowing them to be easily and efficiently used and analysed. We explore three strategies--the pathwise, score function, and measure-valued gradient estimators--exploring their historical development, derivation, and underlying assumptions. We describe their use in other fields, show how they are related and can be combined, and expand on their possible generalisations. Wherever Monte Carlo gradient estimators have been derived and deployed in the past, important advances have followed. A deeper and more widely-held understanding of this problem will lead to further advances, and it is these advances that we wish to support.

Representation Learning for Dynamic Graphs: A Survey

Abstract: Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static graphs. However, many applications involve evolving graphs. This introduces important challenges for learning and inference since nodes, attributes, and edges change over time. In this survey, we review the recent advances in representation learning for dynamic graphs, including dynamic knowledge graphs. We describe existing models from an encoder-decoder perspective, categorize these encoders and decoders based on the techniques they employ, and analyze the approaches in each category. We also review several prominent applications and widely used datasets and highlight directions for future research.

Tslearn, A Machine Learning Toolkit for Time Series Data

Abstract: tslearn is a general-purpose Python machine learning library for time series that offers tools for pre-processing and feature extraction as well as dedicated models for clustering, classification and regression It follows scikit-learn's Application Programming Interface for transformers and estimators, allowing the use of standard pipelines and model selection tools on top of tslearn objects It is distributed under the BSD-2-Clause license, and its source code is available at https://githubcom/tslearn-team/tslearn

Practical Locally Private Heavy Hitters

Abstract: We present new practical local differentially private heavy hitters algorithms achieving optimal or near-optimal worst-case error and running time -- TreeHist and Bitstogram. In both algorithms, server running time is $\tilde O(n)$ and user running time is $\tilde O(1)$, hence improving on the prior state-of-the-art result of Bassily and Smith [STOC 2015] requiring $O(n^{5/2})$ server time and $O(n^{3/2})$ user time. With a typically large number of participants in local algorithms ($n$ in the millions), this reduction in time complexity, in particular at the user side, is crucial for making locally private heavy hitters algorithms usable in practice. We implemented Algorithm TreeHist to verify our theoretical analysis and compared its performance with the performance of Google's RAPPOR code.

New Insights and Perspectives on the Natural Gradient Method

Abstract: Natural gradient descent is an optimization method traditionally motivated from the perspective of information geometry, and works well for many applications as an alternative to stochastic gradient descent. In this paper we critically analyze this method and its properties, and show how it can be viewed as a type of 2nd-order optimization method, with the Fisher information matrix acting as a substitute for the Hessian. In many important cases, the Fisher information matrix is shown to be equivalent to the Generalized Gauss-Newton matrix, which both approximates the Hessian, but also has certain properties that favor its use over the Hessian. This perspective turns out to have significant implications for the design of a practical and robust natural gradient optimizer, as it motivates the use of techniques like trust regions and Tikhonov regularization. Additionally, we make a series of contributions to the understanding of natural gradient and 2nd-order methods, including: a thorough analysis of the convergence speed of stochastic natural gradient descent (and more general stochastic 2nd-order methods) as applied to convex quadratics, a critical examination of the oft-used "empirical" approximation of the Fisher matrix, and an analysis of the (approximate) parameterization invariance property possessed by natural gradient methods (which we show also holds for certain other curvature, but notably not the Hessian).

Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning

Abstract: In many real-world settings, a team of agents must coordinate its behaviour while acting in a decentralised fashion. At the same time, it is often possible to train the agents in a centralised fashion where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a mixing network that estimates joint action-values as a monotonic combination of per-agent values. We structurally enforce that the joint-action value is monotonic in the per-agent values, through the use of non-negative weights in the mixing network, which guarantees consistency between the centralised and decentralised policies. To evaluate the performance of QMIX, we propose the StarCraft Multi-Agent Challenge (SMAC) as a new benchmark for deep multi-agent reinforcement learning. We evaluate QMIX on a challenging set of SMAC scenarios and show that it significantly outperforms existing multi-agent reinforcement learning methods.

scikit-survival: A Library for Time-to-Event Analysis Built on Top of scikit-learn

Abstract: scikit-survival is an open-source Python package for time-to-event analysis fully compatible with scikit-learn. It provides implementations of many popular machine learning techniques for time-to-event analysis, including penalized Cox model, Random Survival Forest, and Survival Support Vector Machine. In addition, the library includes tools to evaluate model performance on censored time-to-event data. The documentation contains installation instructions, interactive notebooks, and a full description of the API. scikit-survival is distributed under the GPL-3 license with the source code and detailed instructions available at https://github.com/sebp/scikit-survival

Joint Causal Inference from Multiple Contexts

Abstract: The gold standard for discovering causal relations is by means of experimentation. Over the last decades, alternative methods have been proposed that can infer causal relations between variables from certain statistical patterns in purely observational data. We introduce Joint Causal Inference (JCI), a novel approach to causal discovery from multiple data sets from different contexts that elegantly unifies both approaches. JCI is a causal modeling framework rather than a specific algorithm, and it can be implemented using any causal discovery algorithm that can take into account certain background knowledge. JCI can deal with different types of interventions (e.g., perfect, imperfect, stochastic, etc.) in a unified fashion, and does not require knowledge of intervention targets or types in case of interventional data. We explain how several well-known causal discovery algorithms can be seen as addressing special cases of the JCI framework, and we also propose novel implementations that extend existing causal discovery methods for purely observational data to the JCI setting. We evaluate different JCI implementations on synthetic data and on flow cytometry protein expression data and conclude that JCI implementations can considerably outperform state-of-the-art causal discovery algorithms.

GluonCV and GluonNLP: Deep Learning in Computer Vision and Natural Language Processing

Abstract: We present GluonCV and GluonNLP, the deep learning toolkits for computer vision and natural language processing based on Apache MXNet (incubating). These toolkits provide state-of-the-art pre-trained models, training scripts, and training logs, to facilitate rapid prototyping and promote reproducible research. We also provide modular APIs with flexible building blocks to enable efficient customization. Leveraging the MXNet ecosystem, the deep learning models in GluonCV and GluonNLP can be deployed onto a variety of platforms with different programming languages. The Apache 2.0 license has been adopted by GluonCV and GluonNLP to allow for software distribution, modification, and usage.

Causal Discovery from Heterogeneous/Nonstationary Data

Abstract: It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time Such a distribution shift feature presents both challenges and opportunities for causal discovery In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism That is, we aim to extract from data a low-dimensional representation of changes The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods

Stochastic Conditional Gradient Methods: From Convex Minimization to Submodular Maximization

Abstract: This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their applicability remains limited when the problem dimension is large and the projection onto a convex set is costly. Instead, stochastic conditional gradient methods are proposed as an alternative solution relying on (i) Approximating gradients via a simple averaging technique requiring a single stochastic gradient evaluation per iteration; (ii) Solving a linear program to compute the descent/ascent direction. The averaging technique reduces the noise of gradient approximations as time progresses, and replacing projection step in proximal methods by a linear program lowers the computational complexity of each iteration. We show that under convexity and smoothness assumptions, our proposed method converges to the optimal objective function value at a sublinear rate of $O(1/t^{1/3})$. Further, for a monotone and continuous DR-submodular function and subject to a general convex body constraint, we prove that our proposed method achieves a $((1-1/e)OPT-\eps)$ guarantee with $O(1/\eps^3)$ stochastic gradient computations. This guarantee matches the known hardness results and closes the gap between deterministic and stochastic continuous submodular maximization. Additionally, we obtain $((1/e)OPT -\eps)$ guarantee after using $O(1/\eps^3)$ stochastic gradients for the case that the objective function is continuous DR-submodular but non-monotone and the constraint set is down-closed. By using stochastic continuous optimization as an interface, we provide the first $(1-1/e)$ tight approximation guarantee for maximizing a monotone but stochastic submodular set function subject to a matroid constraint and $(1/e)$ approximation guarantee for the non-monotone case.

Tuning Hyperparameters without Grad Students: Scalable and Robust Bayesian Optimisation with Dragonfly

Abstract: Bayesian Optimisation (BO) refers to a suite of techniques for global optimisation of expensive black box functions, which use introspective Bayesian models of the function to efficiently search for the optimum While BO has been applied successfully in many applications, modern optimisation tasks usher in new challenges where conventional methods fail spectacularly In this work, we present Dragonfly, an open source Python library for scalable and robust BO Dragonfly incorporates multiple recently developed methods that allow BO to be applied in challenging real world settings; these include better methods for handling higher dimensional domains, methods for handling multi-fidelity evaluations when cheap approximations of an expensive function are available, methods for optimising over structured combinatorial spaces, such as the space of neural network architectures, and methods for handling parallel evaluations Additionally, we develop new methodological improvements in BO for selecting the Bayesian model, selecting the acquisition function, and optimising over complex domains with different variable types and additional constraints We compare Dragonfly to a suite of other packages and algorithms for global optimisation and demonstrate that when the above methods are integrated, they enable significant improvements in the performance of BO The Dragonfly library is available at this http URL

Probabilistic Symmetries and Invariant Neural Networks

Abstract: Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has been devoted to encoding invariance under symmetry transformations into neural network architectures, in an effort to improve the performance of deep neural networks in data-scarce, non-i.i.d., or unsupervised settings. By considering group invariance from the perspective of probabilistic symmetry, we establish a link between functional and probabilistic symmetry, and obtain generative functional representations of probability distributions that are invariant or equivariant under the action of a compact group. Our representations completely characterize the structure of neural networks that can be used to model such distributions and yield a general program for constructing invariant stochastic or deterministic neural networks. We demonstrate that examples from the recent literature are special cases, and develop the details of the general program for exchangeable sequences and arrays.

GraKeL: A Graph Kernel Library in Python

Abstract: The problem of accurately measuring the similarity between graphs is at the core of many applications in a variety of disciplines. Graph kernels have recently emerged as a promising approach to this problem. There are now many kernels, each focusing on different structural aspects of graphs. Here, we present GraKeL, a library that unifies several graph kernels into a common framework. The library is written in Python and adheres to the scikit-learn interface. It is simple to use and can be naturally combined with scikit-learn's modules to build a complete machine learning pipeline for tasks such as graph classification and clustering. The code is BSD licensed and is available at: https://github.com/ysig/ GraKeL.

Reinforcement Learning in Continuous Time and Space: A Stochastic Control Approach

Abstract: We consider reinforcement learning (RL) in continuous time with continuous feature and action spaces. We motivate and devise an exploratory formulation for the feature dynamics that captures learning under exploration, with the resulting optimization problem being a revitalization of the classical relaxed stochastic control. We then study the problem of achieving the best trade-off between exploration and exploitation by considering an entropy-regularized reward function. We carry out a complete analysis of the problem in the linear–quadratic (LQ) setting and deduce that the optimal feedback control distribution for balancing exploitation and exploration is Gaussian. This in turn interprets the widely adopted Gaussian exploration in RL, beyond its simplicity for sampling. Moreover, the exploitation and exploration are captured respectively by the mean and variance of the Gaussian distribution. We characterize the cost of exploration, which, for the LQ case, is shown to be proportional to the entropy regularization weight and inversely proportional to the discount rate. Finally, as the weight of exploration decays to zero, we prove the convergence of the solution of the entropy-regularized LQ problem to the one of the classical LQ problem.

geomstats: a Python Package for Riemannian Geometry in Machine Learning

Abstract: We introduce Geomstats, an open-source Python toolbox for computations and statistics on nonlinear manifolds, such as hyperbolic spaces, spaces of symmetric positive definite matrices, Lie groups of transformations, and many more. We provide object-oriented and extensively unit-tested implementations. Among others, manifolds come equipped with families of Riemannian metrics, with associated exponential and logarithmic maps, geodesics and parallel transport. Statistics and learning algorithms provide methods for estimation, clustering and dimension reduction on manifolds. All associated operations are vectorized for batch computation and provide support for different execution backends, namely NumPy, PyTorch and TensorFlow, enabling GPU acceleration. This paper presents the package, compares it with related libraries and provides relevant code examples. We show that Geomstats provides reliable building blocks to foster research in differential geometry and statistics, and to democratize the use of Riemannian geometry in machine learning applications. The source code is freely available under the MIT license at http://geomstats.ai.

Greedy Attack and Gumbel Attack: Generating Adversarial Examples for Discrete Data

Abstract: We present a probabilistic framework for studying adversarial attacks on discrete data. Based on this framework, we derive a perturbation-based method, Greedy Attack, and a scalable learning-based method, Gumbel Attack, that illustrate various tradeoffs in the design of attacks. We demonstrate the effectiveness of these methods using both quantitative metrics and human evaluation on various state-of-the-art models for text classification, including a word-based CNN, a character-based CNN and an LSTM. As as example of our results, we show that the accuracy of character-based convolutional networks drops to the level of random selection by modifying only five characters through Greedy Attack.

Topology of Deep Neural Networks

Abstract: We study how the topology of a data set $M = M_a \cup M_b \subseteq \mathbb{R}^d$, representing two classes $a$ and $b$ in a binary classification problem, changes as it passes through the layers of a well-trained neural network, i.e., with perfect accuracy on training set and near-zero generalization error ($\approx 0.01\%$). The goal is to shed light on two mysteries in deep neural networks: (i) a nonsmooth activation function like ReLU outperforms a smooth one like hyperbolic tangent; (ii) successful neural network architectures rely on having many layers, even though a shallow network can approximate any function arbitrary well. We performed extensive experiments on the persistent homology of a wide range of point cloud data sets, both real and simulated. The results consistently demonstrate the following: (1) Neural networks operate by changing topology, transforming a topologically complicated data set into a topologically simple one as it passes through the layers. No matter how complicated the topology of $M$ we begin with, when passed through a well-trained neural network $f : \mathbb{R}^d \to \mathbb{R}^p$, there is a vast reduction in the Betti numbers of both components $M_a$ and $M_b$; in fact they nearly always reduce to their lowest possible values: $\beta_k\bigl(f(M_i)\bigr) = 0$ for $k \ge 1$ and $\beta_0\bigl(f(M_i)\bigr) = 1$, $i =a, b$. Furthermore, (2) the reduction in Betti numbers is significantly faster for ReLU activation than hyperbolic tangent activation as the former defines nonhomeomorphic maps that change topology, whereas the latter defines homeomorphic maps that preserve topology. Lastly, (3) shallow and deep networks transform data sets differently -- a shallow network operates mainly through changing geometry and changes topology only in its final layers, a deep one spreads topological changes more evenly across all layers.

pyts: A Python Package for Time Series Classification

Abstract: pyts is an open-source Python package for time series classification. This versatile toolbox provides implementations of many algorithms published in the literature, preprocessing functionalities, and data set loading utilities. pyts relies on the standard scientific Python packages numpy, scipy, scikit-learn, joblib, and numba, and is distributed under the BSD-3-Clause license. Documentation contains installation instructions, a detailed user guide, a full API description, and concrete self-contained examples. Source code and documentation can be downloaded from https://github.com/johannfaouzi/pyts.

Random Smoothing Might be Unable to Certify L∞ Robustness for High-Dimensional Images

Abstract: We show a hardness result for random smoothing to achieve certified adversarial robustness against attacks in the `p ball of radius when p > 2. Although random smoothing has been well understood for the `2 case using the Gaussian distribution, much remains unknown concerning the existence of a noise distribution that works for the case of p > 2. This has been posed as an open problem by Cohen et al. (2019) and includes many significant paradigms such as the `∞ threat model. In this work, we show that any noise distribution D over R that provides `p robustness for all base classifiers with p > 2 must satisfy E η i = Ω(d1−2/p (1− δ)/δ) for 99% of the features (pixels) of vector η ∼ D, where is the robust radius and δ is the score gap between the highest-scored class and the runner-up. Therefore, for high-dimensional images with pixel values bounded in [0, 255], the required noise will eventually dominate the useful information in the images, leading to trivial smoothed classifiers.

A Statistical Learning Approach to Modal Regression

Abstract: This paper studies the nonparametric modal regression problem systematically from a statistical learning view. Originally motivated by pursuing a theoretical understanding of the maximum correntropy criterion based regression (MCCR), our study reveals that MCCR with a tending-to-zero scale parameter is essentially modal regression. We show that nonparametric modal regression problem can be approached via the classical empirical risk minimization. Some efforts are then made to develop a framework for analyzing and implementing modal regression. For instance, the modal regression function is described, the modal regression risk is defined explicitly and its \textit{Bayes} rule is characterized; for the sake of computational tractability, the surrogate modal regression risk, which is termed as the generalization risk in our study, is introduced. On the theoretical side, the excess modal regression risk, the excess generalization risk, the function estimation error, and the relations among the above three quantities are studied rigorously. It turns out that under mild conditions, function estimation consistency and convergence may be pursued in modal regression as in vanilla regression protocols, such as mean regression, median regression, and quantile regression. However, it outperforms these regression models in terms of robustness as shown in our study from a re-descending M-estimation view. This coincides with and in return explains the merits of MCCR on robustness. On the practical side, the implementation issues of modal regression including the computational algorithm and the tuning parameters selection are discussed. Numerical assessments on modal regression are also conducted to verify our findings empirically.

Adaptive Approximation and Generalization of Deep Neural Network with Intrinsic Dimensionality

Abstract: In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs). DNNs generally provide outstanding empirical performance. Hence, numerous studies have actively investigated the theoretical properties of DNNs to understand their underlying mechanisms. In particular, the behavior of DNNs in terms of high-dimensional data is one of the most critical questions. However, this issue has not been sufficiently investigated from the aspect of covariates, although high-dimensional data have practically low intrinsic dimensionality. In this study, we derive bounds for an approximation error and a generalization error regarding DNNs with intrinsically low dimensional covariates. We apply the notion of the Minkowski dimension and develop a novel proof technique. Consequently, we show that convergence rates of the errors by DNNs do not depend on the nominal high dimensionality of data, but on its lower intrinsic dimension. We further prove that the rate is optimal in the minimax sense. We identify an advantage of DNNs by showing that DNNs can handle a broader class of intrinsic low dimensional data than other adaptive estimators. Finally, we conduct a numerical simulation to validate the theoretical results.

Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey

Abstract: Reinforcement learning (RL) is a popular paradigm for addressing sequential decision tasks in which the agent has only limited environmental feedback. Despite many advances over the past three decades, learning in many domains still requires a large amount of interaction with the environment, which can be prohibitively expensive in realistic scenarios. To address this problem, transfer learning has been applied to reinforcement learning such that experience gained in one task can be leveraged when starting to learn the next, harder task. More recently, several lines of research have explored how tasks, or data samples themselves, can be sequenced into a curriculum for the purpose of learning a problem that may otherwise be too difficult to learn from scratch. In this article, we present a framework for curriculum learning (CL) in reinforcement learning, and use it to survey and classify existing CL methods in terms of their assumptions, capabilities, and goals. Finally, we use our framework to find open problems and suggest directions for future RL curriculum learning research.

GADMM: Fast and Communication Efficient Framework for Distributed Machine Learning

Abstract: When the data is distributed across multiple servers, lowering the communication cost between the servers (or workers) while solving the distributed learning problem is an important problem and is the focus of this paper. In particular, we propose a fast, and communication-efficient decentralized framework to solve the distributed machine learning (DML) problem. The proposed algorithm, Group Alternating Direction Method of Multipliers (GADMM) is based on the Alternating Direction Method of Multipliers (ADMM) framework. The key novelty in GADMM is that it solves the problem in a decentralized topology where at most half of the workers are competing for the limited communication resources at any given time. Moreover, each worker exchanges the locally trained model only with two neighboring workers, thereby training a global model with a lower amount of communication overhead in each exchange. We prove that GADMM converges to the optimal solution for convex loss functions, and numerically show that it converges faster and more communication-efficient than the state-of-the-art communication-efficient algorithms such as the Lazily Aggregated Gradient (LAG) and dual averaging, in linear and logistic regression tasks on synthetic and real datasets. Furthermore, we propose Dynamic GADMM (D-GADMM), a variant of GADMM, and prove its convergence under the time-varying network topology of the workers.

Expectation Propagation as a Way of Life: A Framework for Bayesian Inference on Partitioned Data

Abstract: A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need to also split the prior for the local inferences; these weakened priors may not provide enough regularization for each separate computation, thus eliminating one of the key advantages of Bayesian methods. To resolve this dilemma while still retaining the generalizability of the underlying local inference method, we apply the idea of expectation propagation (EP) as a framework for distributed Bayesian inference. The central idea is to iteratively update approximations to the local likelihoods given the state of the other approximations and the prior. The present paper has two roles: we review the steps that are needed to keep EP algorithms numerically stable, and we suggest a general approach, inspired by EP, for approaching data partitioning problems in a way that achieves the computational benefits of parallelism while allowing each local update to make use of relevant information from the other sites. In addition, we demonstrate how the method can be applied in a hierarchical context to make use of partitioning of both data and parameters. The paper describes a general algorithmic framework, rather than a specific algorithm, and presents an example implementation for it.

Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems

Abstract: We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving noise and reward feedback. We show that these methods provably converge to within any pre-specified tolerance of the optimal policy with a number of zero-order evaluations that is an explicit polynomial of the error tolerance, dimension, and curvature properties of the problem. Our analysis reveals some interesting differences between the settings of additive driving noise and random initialization, as well as the settings of one-point and two-point reward feedback. Our theory is corroborated by extensive simulations of derivative-free methods on these systems. Along the way, we derive convergence rates for stochastic zero-order optimization algorithms when applied to a certain class of non-convex problems.

AI Explainability 360: An Extensible Toolkit for Understanding Data and Machine Learning Models

Abstract: As artificial intelligence algorithms make further inroads in high-stakes societal applications, there are increasing calls from multiple stakeholders for these algorithms to explain their outputs. To make matters more challenging, different personas of consumers of explanations have different requirements for explanations. Toward addressing these needs, we introduce AI Explainability 360, an open-source Python toolkit featuring ten diverse and state-of-the-art explainability methods and two evaluation metrics (http://aix360.mybluemix.net). Equally important, we provide a taxonomy to help entities requiring explanations to navigate the space of interpretation and explanation methods, not only those in the toolkit but also in the broader literature on explainability. For data scientists and other users of the toolkit, we have implemented an extensible software architecture that organizes methods according to their place in the AI modeling pipeline. The toolkit is not only the software, but also guidance material, tutorials, and an interactive web demo to introduce AI explainability to different audiences. Together, our toolkit and taxonomy can help identify gaps where more explainability methods are needed and provide a platform to incorporate them as they are developed.

Fast Rates for General Unbounded Loss Functions: From ERM to Generalized Bayes

Abstract: We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to η-generalized Bayesian, MDL, and empirical risk minimization estimators. In the case of log loss, the bounds imply convergence rates for generalized Bayesian inference under misspecification in terms of a generalization of the Hellinger metric as long as the learning rate η is set correctly. For general loss functions, our bounds rely on two separate conditions: the v-GRIP (generalized reversed information projection) conditions, which control the lower tail of the excess loss; and the newly introduced witness condition, which controls the upper tail. The parameter v in the v-GRIP conditions determines the achievable rate and is akin to the exponent in the Tsybakov margin condition and the Bernstein condition for bounded losses, which the v-GRIP conditions generalize; favorable v in combination with small model complexity leads to O(1/n) rates. The witness condition allows us to connect the excess risk to an “annealed” version thereof, by which we generalize several previous results connecting Hellinger and Renyi divergence to KL divergence.