We study the problem of learning graphical models with latent variables. We give the first algorithm for learning locally consistent (ferromagnetic or antiferromagnetic) Restricted Boltzmann Machines (or RBMs) with {\em arbitrary} external fields. Our algorithm has optimal dependence on dimension in the sample complexity and run time however it suffers from a sub-optimal dependency on the underlying parameters of the RBM. Prior results have been established only for {\em ferromagnetic} RBMs with {\em consistent} external fields (signs must be same)\cite{bresler2018learning}. The proposed algorithm strongly relies on the concavity of magnetization which does not hold in our setting. We show the following key structural property: even in the presence of arbitrary external field, for any two observed nodes that share a common latent neighbor, the covariance is high. This enables us to design a simple greedy algorithm that maximizes covariance to iteratively build the neighborhood of each vertex.

Any solution to the "policy learning" problem needs to deal with numerous difficulties, including how to incorporate robustness to potential selection bias as well as fairness constraints articulated by stakeholders, and there have been several notable advances that address these difficulties over the past few years. One limitation of this line of work, however, is that the results cited above all focus on a static setting where a decision-maker only sees each subject once and immediately decides how to treat the subject. In contrast, many problems of applied interest involve a dynamic component whereby the decision-maker makes a series of decisions based on time-varying covariates. In medicine, if a patient has a disease for which all known cures are invasive and have serious side effects, their doctor may choose to monitor disease progression for some time before prescribing one of these invasive treatments. Meanwhile, a health inspector needs to not only choose which restaurants to inspect, but also when to carry out these inspections.

Graphs are a natural abstraction for many problems where nodes represent entities and edges represent a relationship across entities. An important area of research that has emerged over the last decade is the use of graphs as a vehicle for non-linear dimensionality reduction in a manner akin to previous efforts based on manifold learning with uses for downstream database processing, machine learning and visualization. In this systematic yet comprehensive experimental survey, we benchmark several popular network representation learning methods operating on two key tasks: link prediction and node classification. We examine the performance of 12 unsupervised embedding methods on 15 datasets. To the best of our knowledge, the scale of our study -- both in terms of the number of methods and number of datasets -- is the largest to date. Our results reveal several key insights about work-to-date in this space. First, we find that certain baseline methods (task-specific heuristics, as well as classic manifold methods) that have often been dismissed or are not considered by previous efforts can compete on certain types of datasets if they are tuned appropriately. Second, we find that recent methods based on matrix factorization offer a small but relatively consistent advantage over alternative methods (e.g., random-walk based methods) from a qualitative standpoint. Specifically, we find that MNMF, a community preserving embedding method, is the most competitive method for the link prediction task. While NetMF is the most competitive baseline for node classification. Third, no single method completely outperforms other embedding methods on both node classification and link prediction tasks. We also present several drill-down analysis that reveals settings under which certain algorithms perform well (e.g., the role of neighborhood context on performance) -- guiding the end-user.

In a multi-agent pathfinding (MAPF) problem, agents need to navigate from their start to their goal locations without colliding into each other. There are various MAPF algorithms, including Windowed Hierarchical Cooperative A*, Flow Annotated Replanning, and Bounded Multi-Agent A*. It is often the case that there is no a single algorithm that dominates all MAPF instances. Therefore, in this paper, we investigate the use of deep learning to automatically select the best MAPF algorithm from a portfolio of algorithms for a given MAPF problem instance. Empirical results show that our automatic algorithm selection approach, which uses an off-the-shelf convolutional neural network, is able to outperform any individual MAPF algorithm in our portfolio.

Aggregating multi-subject fMRI data is indispensable for generating valid and general inferences from patterns distributed across human brains. The disparities in anatomical structures and functional topographies of human brains call for aligning fMRI data across subjects. However, the existing functional alignment methods cannot tackle various kinds of fMRI datasets today, especially when they are incomplete, i.e., some of the subjects probably lack the responses to some stimuli, or different subjects might follow different sequences of stimuli. In this paper, a cross-subject graph that depicts the (dis)similarities between samples across subjects is taken as prior information for developing a more flexible framework that suits an assortment of fMRI datasets. However, the high dimension of fMRI data and the use of multiple subjects makes the crude framework time-consuming or unpractical. Therefore, we regularize the framework so that a feasible kernel-based optimization, which permits non-linear feature extraction, could be theoretically developed. Specifically, a low-dimension assumption is imposed on each new feature space to avoid overfitting caused by the high-spatial-low-temporal resolution of fMRI data. Empirical studies confirm that the proposed method under both incompleteness and completeness can achieve better performance than other state-of-the-art functional alignment methods under completeness.

Large capacity machine learning models are prone to membership inference attacks in which an adversary aims to infer whether a particular data sample is a member of the target model's training dataset. Such membership inferences can lead to serious privacy violations as machine learning models are often trained using privacy-sensitive data such as medical records and controversial user opinions. Recently defenses against membership inference attacks are developed, in particular, based on differential privacy and adversarial regularization; unfortunately, such defenses highly impact the classification accuracy of the underlying machine learning models. In this work, we present a new defense against membership inference attacks that preserves the utility of the target machine learning models significantly better than prior defenses. Our defense, called distillation for membership privacy (DMP), leverages knowledge distillation, a model compression technique, to train machine learning models with membership privacy. We use different techniques in the DMP to maximize its membership privacy with minor degradation to utility. DMP works effectively against the attackers with either a whitebox or blackbox access to the target model. We evaluate DMP's performance through extensive experiments on different deep neural networks and using various benchmark datasets. We show that DMP provides a significantly better tradeoff between inference resilience and classification performance than state-of-the-art membership inference defenses. For instance, a DMP-trained DenseNet provides a classification accuracy of 65.3\% for a 54.4\% (54.7\%) blackbox (whitebox) membership inference attack accuracy, while an adversarially regularized DenseNet provides a classification accuracy of only 53.7\% for a (much worse) 68.7\% (69.5\%) blackbox (whitebox) membership inference attack accuracy.

Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data, which has received the most attention in the literature, in this paper we will review how Bayesian networks can model dynamic data and data with incomplete observations. Such data are the norm at the forefront of research and applications, and Bayesian networks are uniquely positioned to model them due to their explainability and interpretability.

Heuristic algorithms such as simulated annealing, Concorde, and METIS are effective and widely used approaches to find solutions to combinatorial optimization problems. However, they are limited by the high sample complexity required to reach a reasonable solution from a cold-start. In this paper, we introduce a novel framework to generate better initial solutions for heuristic algorithms using reinforcement learning (RL), named RLHO. We augment the ability of heuristic algorithms to greedily improve upon an existing initial solution generated by RL, and demonstrate novel results where RL is able to leverage the performance of heuristics as a learning signal to generate better initialization. We apply this framework to Proximal Policy Optimization (PPO) and Simulated Annealing (SA). We conduct a series of experiments on the well-known NP-complete bin packing problem, and show that the RLHO method outperforms our baselines. We show that on the bin packing problem, RL can learn to help heuristics perform even better, allowing us to combine the best parts of both approaches.

We study the robustness verification problem for tree-based models, including decision trees, random forests (RFs) and gradient boosted decision trees (GBDTs). Formal robustness verification of decision tree ensembles involves finding the exact minimal adversarial perturbation or a guaranteed lower bound of it. Existing approaches find the minimal adversarial perturbation by a mixed integer linear programming (MILP) problem, which takes exponential time so is impractical for large ensembles. Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles, the verification problem can be cast as a max-clique problem on a multi-partite graph with bounded boxicity. For low dimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm. For general problems, by exploiting the boxicity of the graph, we develop an efficient multi-level verification algorithm that can give tight lower bounds on the robustness of decision tree ensembles, while allowing iterative improvement and any-time termination. OnRF/GBDT models trained on 10 datasets, our algorithm is hundreds of times faster than the previous approach that requires solving MILPs, and is able to give tight robustness verification bounds on large GBDTs with hundreds of deep trees.

We consider two multi-armed bandit problems with $n$ arms: (i) given an $\epsilon > 0$, identify an arm with mean that is within $\epsilon$ of the largest mean and (ii) given a threshold $\mu_0$ and integer $k$, identify $k$ arms with means larger than $\mu_0$. Existing lower bounds and algorithms for the PAC framework suggest that both of these problems require $\Omega(n)$ samples. However, we argue that these definitions not only conflict with how these algorithms are used in practice, but also that these results disagree with intuition that says (i) requires only $\Theta(\frac{n}{m})$ samples where $m = |\{ i : \mu_i > \max_{i \in [n]} \mu_i - \epsilon\}|$ and (ii) requires $\Theta(\frac{n}{m}k)$ samples where $m = |\{ i : \mu_i > \mu_0 \}|$. We provide definitions that formalize these intuitions, obtain lower bounds that match the above sample complexities, and develop explicit, practical algorithms that achieve nearly matching upper bounds.