Individuals do not respond uniformly to treatments, events, or interventions. Sociologists routinely partition samples into subgroups to explore how the effects of treatments vary by covariates like race, gender, and socioeconomic status. In so doing, analysts determine the key subpopulations based on theoretical priors. Data-driven discoveries are also routine, yet the analyses by which sociologists typically go about them are problematic and seldom move us beyond our expectations, and biases, to explore new meaningful subgroups. Emerging machine learning methods allow researchers to explore sources of variation that they may not have previously considered, or envisaged. In this paper, we use causal trees to recursively partition the sample and uncover sources of treatment effect heterogeneity. We use honest estimation, splitting the sample into a training sample to grow the tree and an estimation sample to estimate leaf-specific effects. Assessing a central topic in the social inequality literature, college effects on wages, we compare what we learn from conventional approaches for exploring variation in effects to causal trees. Given our use of observational data, we use leaf-specific matching and sensitivity analyses to address confounding and offer interpretations of effects based on observed and unobserved heterogeneity. We encourage researchers to follow similar practices in their work on variation in sociological effects.

Discrete random variables are natural components of probabilistic clustering models. A number of VAE variants with discrete latent variables have been developed. Training such methods requires marginalizing over the discrete latent variables, causing training time complexity to be linear in the number clusters. By applying a continuous relaxation to the discrete variables in these methods we can achieve a reduction in the training time complexity to be constant in the number of clusters used. We demonstrate that in practice for one such method, the Gaussian Mixture VAE, the use of a continuous relaxation has no negative effect on the quality of the clustering but provides a substantial reduction in training time, reducing training time on CIFAR-100 with 20 clusters from 47 hours to less than 6 hours.

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose several variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, the experimental results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.

--Clustering is a crucial component of many data mining systems involving the analysis and exploration of various data. Data diversity calls for clustering algorithms to be accurate while providing stable (i.e., deterministic and robust) results on arbitrary input networks. Moreover, modern systems often operate with large datasets, which implicitly constrains the complexity of the clustering algorithm. Existing clustering techniques are only partially stable, however, as they guarantee either determinism or robustness. T o address this issue, we introduce DAOC, a Deterministic and Agglomerative Overlapping Clustering algorithm. DAOC leverages a new technique called Overlap Decomposition to identify fine-grained clusters in a deterministic way capturing multiple optima. In addition, it leverages a novel consensus approach, Mutual Maximal Gain, to ensure robustness and further improve the stability of the results while still being capable of identifying micro-scale clusters. Our empirical results on both synthetic and real-world networks show that DAOC yields stable clusters while being on average 25% more accurate than state-of-the-art deterministic algorithms without requiring any tuning. Our approach has the ambition to greatly simplify and speed up data analysis tasks involving iterative processing (need for determinism) as well as data fluctuations (need for robustness) and to provide accurate and reproducible results. Clustering is a fundamental part of data mining with a wide applicability to statistical analysis and exploration of physical, social, biological and informational systems.

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the robust statistics approach to consider perturbations under any Wasserstein distance, and show that robust estimation is possible whenever a distribution's population statistics are robust under a certain family of friendly perturbations. This generalizes a property called resilience previously employed in the special case of mean estimation with outliers. We justify the generalized resilience property by showing that it holds under moment or hypercontractive conditions. Even in the total variation case, these subsume conditions in the literature for mean estimation, regression, and covariance estimation; the resulting analysis simplifies and sometimes improves these known results in both population limit and finite-sample rate. Our robust estimators are based on minimum distance (MD) functionals (Donoho and Liu, 1988), which project onto a set of distributions under a discrepancy related to the perturbation. We present two approaches for designing MD estimators with good finite-sample rates: weakening the discrepancy and expanding the set of distributions. We also present connections to Gao et al. (2019)'s recent analysis of generative adversarial networks for robust estimation.

A variety of applications spanning science and engineering use Markov reward processes as models for real-world phenomena, including queueing systems, transportation networks, robotic exploration, game playing, and epidemiology. In some of these settings, the underlying parameters that govern the process are known to the modeller, but in others, these must be estimated from observed data. A salient example of the latter setting, which forms the main motivation for this paper, is the policy evaluation problem encountered in Markov decision processes (MDPs) and reinforcement learning [Ber95a; Ber95b; SB18]. Here an agent operates in an environment whose dynamics are unknown: at each step, it observes the current state of the environment, and takes an action that changes its state according to some stochastic transition function determined by the environment. The goal is to evaluate the utility of some policy--that is, a mapping from states to actions, where utility is measured using rewards that the agent receives from the environment. These rewards are usually assumed to be additive over time, and since the policy determines the action to be taken at each state, the reward obtained at any time is simply a function of the current state of the agent. Thus, this setting induces a Markov reward process (MRP) on the state space, in which both the underlying transitions and rewards are unknown to the agent. The agent only observes samples of state transitions and rewards. 1

Improving the sample efficiency in reinforcement learning has been a long-standing research problem. In this work, we aim to reduce the sample complexity of existing policy gradient methods. We propose a novel policy gradient algorithm called SRVR-PG, which only requires $O(1/\epsilon^{3/2})$ episodes to find an $\epsilon$-approximate stationary point of the nonconcave performance function $J(\boldsymbol{\theta})$ (i.e., $\boldsymbol{\theta}$ such that $\|\nabla J(\boldsymbol{\theta})\|_2^2\leq\epsilon$). This sample complexity improves the best known result $O(1/\epsilon^{5/3})$ for policy gradient algorithms by a factor of $O(1/\epsilon^{1/6})$. In addition, we also propose a variant of SRVR-PG with parameter exploration, which explores the initial policy parameter from a prior probability distribution. We conduct numerical experiments on classic control problems in reinforcement learning to validate the performance of our proposed algorithms.

This study combines two different learning paradigms, k-nearest neighbor (k-NN) rule, as memory-based learning paradigm and relevance vector machines (RVM), as statistical learning paradigm. This combination is performed in kernel space and is called k-relevance vector (k-RV). The purpose is to improve the performance of k-NN rule. The proposed model significantly prunes irrelevant attributes. We also introduced a new parameter, responsible for early stopping of iterations in RVM. We show that the new parameter improves the classification accuracy of k-RV. Intensive experiments are conducted on several classification datasets from University of California Irvine (UCI) repository and two real datasets from computer vision domain. The performance of k-RV is highly competitive compared to a few state-of-the-arts in terms of classification accuracy.

As machine learning (ML) becomes more and more powerful and easily accessible, attackers increasingly leverage ML to perform automated large-scale inference attacks in various domains. In such an ML-equipped inference attack, an attacker has access to some data (called public data) of an individual, a software, or a system; and the attacker uses an ML classifier to automatically infer their private data. Inference attacks pose severe privacy and security threats to individuals and systems. Inference attacks are successful because private data are statistically correlated with public data, and ML classifiers can capture such statistical correlations. In this chapter, we discuss the opportunities and challenges of defending against ML-equipped inference attacks via adversarial examples. Our key observation is that attackers rely on ML classifiers in inference attacks. The adversarial machine learning community has demonstrated that ML classifiers have various vulnerabilities. Therefore, we can turn the vulnerabilities of ML into defenses against inference attacks. For example, ML classifiers are vulnerable to adversarial examples, which add carefully crafted noise to normal examples such that an ML classifier makes predictions for the examples as we desire. To defend against inference attacks, we can add carefully crafted noise into the public data to turn them into adversarial examples, such that attackers' classifiers make incorrect predictions for the private data. However, existing methods to construct adversarial examples are insufficient because they did not consider the unique challenges and requirements for the crafted noise at defending against inference attacks. In this chapter, we take defending against inference attacks in online social networks as an example to illustrate the opportunities and challenges.

In machine learning we often try to optimise a decision rule that would have worked well over a historical dataset; this is the so called empirical risk minimisation principle. In the context of learning from recommender system logs, applying this principle becomes a problem because we do not have available the reward of decisions we did not do. In order to handle this "bandit-feedback" setting, several Counterfactual Risk Minimisation (CRM) methods have been proposed in recent years, that attempt to estimate the performance of different policies on historical data. Through importance sampling and various variance reduction techniques, these methods allow more robust learning and inference than classical approaches. It is difficult to accurately estimate the performance of policies that frequently perform actions that were infrequently done in the past and a number of different types of estimators have been proposed. In this paper, we review several methods, based on different off-policy estimators, for learning from bandit feedback. We discuss key differences and commonalities among existing approaches, and compare their empirical performance on the RecoGym simulation environment. To the best of our knowledge, this work is the first comparison study for bandit algorithms in a recommender system setting.