We introduce a framework for dynamic adversarial discovery of information (DADI), motivated by a scenario where information (a feature set) is used by third parties with unknown objectives. We train a reinforcement learning agent to sequentially acquire a subset of the information while balancing accuracy and fairness of predictors downstream. Based on the set of already acquired features, the agent decides dynamically to either collect more information from the set of available features or to stop and predict using the information that is currently available. Building on previous work exploring adversarial representation learning, we attain group fairness (demographic parity) by rewarding the agent with the adversary's loss, computed over the final feature set. Importantly, however, the framework provides a more general starting point for fair or private dynamic information discovery. Finally, we demonstrate empirically, using two real-world datasets, that we can trade-off fairness and predictive performance

The use of momentum in stochastic gradient methods has become a widespread practice in machine learning. Different variants of momentum, including heavy-ball momentum, Nesterov's accelerated gradient (NAG), and quasi-hyperbolic momentum (QHM), have demonstrated success on various tasks. Despite these empirical successes, there is a lack of clear understanding of how the momentum parameters affect convergence and various performance measures of different algorithms. In this paper, we use the general formulation of QHM to give a unified analysis of several popular algorithms, covering their asymptotic convergence conditions, stability regions, and properties of their stationary distributions. In addition, by combining the results on convergence rates and stationary distributions, we obtain sometimes counter-intuitive practical guidelines for setting the learning rate and momentum parameters.

We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each individual graph layer. We propose a regularizer based on the generalized matrix mean, which is a one-parameter family of matrix means that includes the arithmetic, geometric and harmonic means as particular cases. We analyze it in expectation under a Multilayer Stochastic Block Model and verify numerically that it outperforms state of the art methods. Moreover, we introduce a matrix-free numerical scheme based on contour integral quadratures and Krylov subspace solvers that scales to large sparse multilayer graphs.

Machine learning has proved to be very successful for making predictions in travel behavior modeling. However, most machine-learning models have complex model structures and offer little or no explanation as to how they arrive at these predictions. Interpretations about travel behavior models are essential for decision makers to understand travelers' preferences and plan policy interventions accordingly. Therefore, this paper proposes to apply and extend the model distillation approach, a model-agnostic machine-learning interpretation method, to explain how a black-box travel mode choice model makes predictions for the entire population and subpopulations of interest. Model distillation aims at compressing knowledge from a complex model (teacher) into an understandable and interpretable model (student). In particular, the paper integrates model distillation with market segmentation to generate more insights by accounting for heterogeneity. Furthermore, the paper provides a comprehensive comparison of student models with the benchmark model (decision tree) and the teacher model (gradient boosting trees) to quantify the fidelity and accuracy of the students' interpretations.

We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*, adapted to a probabilistic setting with noise. The key insight is the use of conditional probabilities for observations, and the introduction of a local tolerance when comparing them. When applied to RNNs, our algorithm often achieves better word error rate (WER) and normalised distributed cumulative gain (NDCG) than that achieved by spectral extraction of weighted finite automata (WFA) from the same networks. PDFAs are substantially more expressive than n-grams, and are guaranteed to be stochastic and deterministic - unlike spectrally extracted WFAs.

We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems when processing discrete-time inputs under various hypotheses on their dependence structure. Non-asymptotic bounds are explicitly written down in terms of the multivariate Rademacher complexities of the reservoir systems and the weak dependence structure of the signals that are being handled. This allows, in particular, to determine the minimal number of observations needed in order to guarantee a prescribed estimation accuracy with high probability for a given reservoir family. At the same time, the asymptotic behavior of the devised bounds guarantees the consistency of the empirical risk minimization procedure for various hypothesis classes of reservoir functionals.

Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of agents) relative to non-cooperative approaches in the strongly-convex setting. More recently, these results have been extended to the pursuit of first-order stationary points in non-convex environments. In this work, we examine in detail the dependence of second-order convergence guarantees on the spectral properties of the combination policy for non-convex multi agent optimization. We establish linear speedup in saddle-point escape time in the number of agents for symmetric combination policies and study the potential for further improvement by employing asymmetric combination weights. The results imply that a linear speedup can be expected in the pursuit of second-order stationary points, which exclude local maxima as well as strict saddle-points and correspond to local or even global minima in many important learning settings.

Markov networks are widely studied and used throughout multivariate statistics and computer science. In particular, the problem of learning the structure of Markov networks from data without invoking chordality assumptions in order to retain expressiveness of the model class has been given a considerable attention in the recent literature, where numerous constraint-based or score-based methods have been introduced. Here we develop a new search algorithm for the network score-optimization that has several computational advantages and scales well to high-dimensional data sets. The key observation behind the algorithm is that the neighborhood of a variable can be efficiently captured using local penalized likelihood ratio (PLR) tests by exploiting an exponential decay of correlations across the neighborhood with an increasing graph-theoretic distance from the focus node. The candidate neighborhoods are then processed by a two-stage hill-climbing (HC) algorithm. Our approach, termed fully as PLRHC-BIC$_{0.5}$, compares favorably against the state-of-the-art methods in all our experiments spanning both low- and high-dimensional networks and a wide range of sample sizes. An efficient implementation of PLRHC-BIC$_{0.5}$ is freely available from the URL: https://github.com/jurikuronen/plrhc.

We demonstrate how machine learning is able to model experiments in quantum physics. Quantum entanglement is a cornerstone for upcoming quantum technologies such as quantum computation and quantum cryptography. Of particular interest are complex quantum states with more than two particles and a large number of entangled quantum levels. Given such a multiparticle high-dimensional quantum state, it is usually impossible to reconstruct an experimental setup that produces it. To search for interesting experiments, one thus has to randomly create millions of setups on a computer and calculate the respective output states. In this work, we show that machine learning models can provide significant improvement over random search. We demonstrate that a long short-term memory (LSTM) neural network can successfully learn to model quantum experiments by correctly predicting output state characteristics for given setups without the necessity of computing the states themselves. This approach not only allows for faster search but is also an essential step towards automated design of multiparticle high-dimensional quantum experiments using generative machine learning models.

Unitary recurrent neural networks (URNNs) have been proposed as a method to overcome the vanishing and exploding gradient problem in modeling data with long-term dependencies. A basic question is how restrictive is the unitary constraint on the possible input-output mappings of such a network? This work shows that for any contractive RNN with ReLU activations, there is a URNN with at most twice the number of hidden states and the identical input-output mapping. Hence, with ReLU activations, URNNs are as expressive as general RNNs. In contrast, for certain smooth activations, it is shown that the input-output mapping of an RNN cannot be matched with a URNN, even with an arbitrary number of states. The theoretical results are supported by experiments on modeling of slowly-varying dynamical systems.