Increasingly complex generative models are being used across disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to evaluate the likelihood function and thus to perform likelihood-based statistical inference. A likelihood-free inference framework has emerged where the parameters are identified by finding values that yield simulated data resembling the observed data. While widely applicable, a major difficulty in this framework is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models. We validate our approach using theory and simulations for both point estimation and Bayesian inference, and demonstrate its use on real data by inferring an individual-based epidemiological model for bacterial infections in child care centers.

Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning. In this paper we dramatically simplify the support function representation for GMF functions as well as the representation of their subdifferentials. These new representations allow the ready computation of a range of important related geometric objects whose formulations were previously unavailable.

We study contextual multi-armed bandit problems under linear realizability on rewards and uncertainty (or noise) on features. For the case of identical noise on features across actions, we propose an algorithm, coined {\em NLinRel}, having $O\left(T^{\frac{7}{8}} \left(\log{(dT)}+K\sqrt{d}\right)\right)$ regret bound for $T$ rounds, $K$ actions, and $d$-dimensional feature vectors. Next, for the case of non-identical noise, we observe that popular linear hypotheses including {\em NLinRel} are impossible to achieve such sub-linear regret. Instead, under assumption of Gaussian feature vectors, we prove that a greedy algorithm has $O\left(T^{\frac23}\sqrt{\log d}\right)$ regret bound with respect to the optimal linear hypothesis. Utilizing our theoretical understanding on the Gaussian case, we also design a practical variant of {\em NLinRel}, coined {\em Universal-NLinRel}, for arbitrary feature distributions. It first runs {\em NLinRel} for finding the `true' coefficient vector using feature uncertainties and then adjust it to minimize its regret using the statistical feature information. We justify the performance of {\em Universal-NLinRel} on both synthetic and real-world datasets.

Poisoning attack is identified as a severe security threat to machine learning algorithms. In many applications, for example, deep neural network (DNN) models collect public data as the inputs to perform re-training, where the input data can be poisoned. Although poisoning attack against support vector machines (SVM) has been extensively studied before, there is still very limited knowledge about how such attack can be implemented on neural networks (NN), especially DNNs. In this work, we first examine the possibility of applying traditional gradient-based method (named as the direct gradient method) to generate poisoned data against NNs by leveraging the gradient of the target model w.r.t. the normal data. We then propose a generative method to accelerate the generation rate of the poisoned data: an auto-encoder (generator) used to generate poisoned data is updated by a reward function of the loss, and the target NN model (discriminator) receives the poisoned data to calculate the loss w.r.t. the normal data. Our experiment results show that the generative method can speed up the poisoned data generation rate by up to 239.38x compared with the direct gradient method, with slightly lower model accuracy degradation. A countermeasure is also designed to detect such poisoning attack methods by checking the loss of the target model.

Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many hardness results are known. In this paper we propose a provably polynomial-time algorithm for learning sparse Gaussian Bayesian networks with equal noise variance --- a class of Bayesian networks for which the DAG structure can be uniquely identified from observational data --- under high-dimensional settings. We show that $O(k^4 \log p)$ number of samples suffices for our method to recover the true DAG structure with high probability, where $p$ is the number of variables and $k$ is the maximum Markov blanket size. We obtain our theoretical guarantees under a condition called Restricted Strong Adjacency Faithfulness, which is strictly weaker than strong faithfulness --- a condition that other methods based on conditional independence testing need for their success. The sample complexity of our method matches the information-theoretic limits in terms of the dependence on $p$. We show that our method out-performs existing state-of-the-art methods for learning Gaussian Bayesian networks in terms of recovering the true DAG structure while being comparable in speed to heuristic methods.

Machine learning methods in general and Deep Neural Networks in particular have shown to be vulnerable to adversarial perturbations. So far this phenomenon has mainly been studied in the context of whole-image classification. In this contribution, we analyse how adversarial perturbations can affect the task of semantic segmentation. We show how existing adversarial attackers can be transferred to this task and that it is possible to create imperceptible adversarial perturbations that lead a deep network to misclassify almost all pixels of a chosen class while leaving network prediction nearly unchanged outside this class.

This note is concerned with accurate and computationally efficient approximations of moments of Gaussian random variables passed through sigmoid or softmax mappings. These approximations are semi-analytical (i.e. they involve the numerical adjustment of parametric forms) and highly accurate (they yield 5% error at most). We also highlight a few niche applications of these approximations, which arise in the context of, e.g., drift-diffusion models of decision making or non-parametric data clustering approaches. We provide these as examples of efficient alternatives to more tedious derivations that would be needed if one was to approach the underlying mathematical issues in a more formal way. We hope that this technical note will be helpful to modellers facing similar mathematical issues, although maybe stemming from different academic prospects.

Two potential bottlenecks on the expressiveness of recurrent neural networks (RNNs) are their ability to store information about the task in their parameters, and to store information about the input history in their units. We show experimentally that all common RNN architectures achieve nearly the same per-task and per-unit capacity bounds with careful training, for a variety of tasks and stacking depths. They can store an amount of task information which is linear in the number of parameters, and is approximately 5 bits per parameter. They can additionally store approximately one real number from their input history per hidden unit. We further find that for several tasks it is the per-task parameter capacity bound that determines performance. These results suggest that many previous results comparing RNN architectures are driven primarily by differences in training effectiveness, rather than differences in capacity. Supporting this observation, we compare training difficulty for several architectures, and show that vanilla RNNs are far more difficult to train, yet have slightly higher capacity. Finally, we propose two novel RNN architectures, one of which is easier to train than the LSTM or GRU for deeply stacked architectures.

Safety is a desirable property that can immensely increase the applicability of learning algorithms in real-world decision-making problems. It is much easier for a company to deploy an algorithm that is safe, i.e., guaranteed to perform at least as well as a baseline. In this paper, we study the issue of safety in contextual linear bandits that have application in many different fields including personalized ad recommendation in online marketing. We formulate a notion of safety for this class of algorithms. We develop a safe contextual linear bandit algorithm, called conservative linear UCB (CLUCB), that simultaneously minimizes its regret and satisfies the safety constraint, i.e., maintains its performance above a fixed percentage of the performance of a baseline strategy, uniformly over time. We prove an upper-bound on the regret of CLUCB and show that it can be decomposed into two terms: 1) an upper-bound for the regret of the standard linear UCB algorithm that grows with the time horizon and 2) a constant (does not grow with the time horizon) term that accounts for the loss of being conservative in order to satisfy the safety constraint. We empirically show that our algorithm is safe and validate our theoretical analysis.

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solver over polytopes, thereby partially answering a 30 year-old conjecture. We also survey other convergence results and highlight gaps in the theoretical underpinnings of FW-style algorithms. Motivating applications without known efficient alternatives are explored through structured prediction with combinatorial penalties as well as games over matching polytopes involving an exponential number of constraints.