We consider the problem of active feature acquisition where the goal is to sequentially select the subset of features in order to achieve the maximum prediction performance in the most cost-effective way at test time. In this work, we formulate this active feature acquisition as a jointly learning problem of training both the classifier (environment) and the RL agent that decides either to `stop and predict' or `collect a new feature' at test time, in a cost-sensitive manner. We also introduce a novel encoding scheme to represent acquired subsets of features by proposing an order-invariant set encoding at the feature level, which also significantly reduces the search space for our agent. We evaluate our model on a carefully designed synthetic dataset for the active feature acquisition as well as several medical datasets. Our framework shows meaningful feature acquisition process for diagnosis that complies with human knowledge, and outperforms all baselines in terms of prediction performance as well as feature acquisition cost.

This paper examines the long-run behavior of learning with bandit feedback in non-cooperative concave games. The bandit framework accounts for extremely low-information environments where the agents may not even know they are playing a game; as such, the agents’ most sensible choice in this setting would be to employ a no-regret learning algorithm. In general, this does not mean that the players' behavior stabilizes in the long run: no-regret learning may lead to cycles, even with perfect gradient information. However, if a standard monotonicity condition is satisfied, our analysis shows that no-regret learning based on mirror descent with bandit feedback converges to Nash equilibrium with probability 1. We also derive an upper bound for the convergence rate of the process that nearly matches the best attainable rate for single-agent bandit stochastic optimization.

Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range bounded in $[0,1]$, the generalization error of $\gamma$-uniformly stable learning algorithm on $n$ samples is known to be at most $O((\gamma +1/n) \sqrt{n \log(1/\delta)})$ with probability at least $1-\delta$. Unfortunately, this bound does not lead to meaningful generalization bounds in many common settings where $\gamma \geq 1/\sqrt{n}$. At the same time the bound is known to be tight only when $\gamma = O(1/n)$. Here we prove substantially stronger generalization bounds for uniformly stable algorithms without any additional assumptions. First, we show that the generalization error in this setting is at most $O(\sqrt{(\gamma + 1/n) \log(1/\delta)})$ with probability at least $1-\delta$. In addition, we prove a tight bound of $O(\gamma^2 + 1/n)$ on the second moment of the generalization error. The best previous bound on the second moment of the generalization error is $O(\gamma + 1/n)$. Our proofs are based on new analysis techniques and our results imply substantially stronger generalization guarantees for several well-studied algorithms.

We often desire our models to be interpretable as well as accurate. Prior work on optimizing models for interpretability has relied on easy-to-quantify proxies for interpretability, such as sparsity or the number of operations required. In this work, we optimize for interpretability by directly including humans in the optimization loop. We develop an algorithm that minimizes the number of user studies to find models that are both predictive and interpretable and demonstrate our approach on several data sets. Our human subjects results show trends towards different proxy notions of interpretability on different datasets, which suggests that different proxies are preferred on different tasks.

Stochastic gradient hard thresholding methods have recently been shown to work favorably in solving large-scale empirical risk minimization problems under sparsity or rank constraint. Despite the improved iteration complexity over full gradient methods, the gradient evaluation and hard thresholding complexity of the existing stochastic algorithms usually scales linearly with data size, which could still be expensive when data is huge and the hard thresholding step could be as expensive as singular value decomposition in rank-constrained problems. To address these deficiencies, we propose an efficient hybrid stochastic gradient hard thresholding (HSG-HT) method that can be provably shown to have sample-size-independent gradient evaluation and hard thresholding complexity bounds. Specifically, we prove that the stochastic gradient evaluation complexity of HSG-HT scales linearly with inverse of sub-optimality and its hard thresholding complexity scales logarithmically. By applying the heavy ball acceleration technique, we further propose an accelerated variant of HSG-HT which can be shown to have improved factor dependence on restricted condition number in the quadratic case. Numerical results confirm our theoretical affirmation and demonstrate the computational efficiency of the proposed methods.

To date, research effort has largely focussed on the development of Bayesian cubature, whose distributional output provides uncertainty quantification for the integral. However, the point estimators associated to Bayesian cubature can be inaccurate and acutely sensitive to the prior when the domain is high-dimensional. To address these drawbacks we introduce Bayes-Sard cubature, a probabilistic framework that combines the flexibility of Bayesian cubature with the robustness of classical cubatures which are well-established. This is achieved by considering a Gaussian process model for the integrand whose mean is a parametric regression model, with an improper prior on each regression coefficient. The features in the regression model consist of test functions which are guaranteed to be exactly integrated, with remaining degrees of freedom afforded to the non-parametric part. The asymptotic convergence of the Bayes-Sard cubature method is established and the theoretical results are numerically verified. In particular, we report two orders of magnitude reduction in error compared to Bayesian cubature in the context of a high-dimensional financial integral.

Estimating individual treatment effect (ITE) is a challenging problem in causal inference, due to the missing counterfactuals and the selection bias. Existing ITE estimation methods mainly focus on balancing the distributions of control and treated groups, but ignore the local similarity information that is helpful. In this paper, we propose a local similarity preserved individual treatment effect (SITE) estimation method based on deep representation learning. SITE preserves local similarity and balances data distributions simultaneously, by focusing on several hard samples in each mini-batch. Experimental results on synthetic and three real-world datasets demonstrate the advantages of the proposed SITE method, compared with the state-of-the-art ITE estimation methods.

We propose a novel class of network models for temporal dyadic interaction data. Our objective is to capture important features often observed in social interactions: sparsity, degree heterogeneity, community structure and reciprocity. We use mutually-exciting Hawkes processes to model the interactions between each (directed) pair of individuals. The intensity of each process allows interactions to arise as responses to opposite interactions (reciprocity), or due to shared interests between individuals (community structure). For sparsity and degree heterogeneity, we build the non time dependent part of the intensity function on compound random measures following Todeschini et al., 2016. We conduct experiments on real-world temporal interaction data and show that the proposed model outperforms competing approaches for link prediction, and leads to interpretable parameters.

Symmetric nonnegative matrix factorization (NMF)---a special but important class of the general NMF---is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for Symmetric NMF is not as easy as for the nonsymmetric counterpart, the latter admitting the splitting property that allows efficient alternating-type algorithms. To overcome this issue, we transfer the symmetric NMF to a nonsymmetric one, then we can adopt the idea from the state-of-the-art algorithms for nonsymmetric NMF to design fast algorithms solving symmetric NMF. We rigorously establish that solving nonsymmetric reformulation returns a solution for symmetric NMF and then apply fast alternating based algorithms for the corresponding reformulated problem. Furthermore, we show these fast algorithms admit strong convergence guarantee in the sense that the generated sequence is convergent at least at a sublinear rate and it converges globally to a critical point of the symmetric NMF. We conduct experiments on both synthetic data and image clustering to support our result.

Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that they may cycle, and there is no good understanding of their limit points when they do not. When they converge, do they converge to local min-max solutions? We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent Ascent (OGDA). We show that both dynamics avoid unstable critical points for almost all initializations. Moreover, for small step sizes and under mild assumptions, the set of OGDA-stable critical points is a superset of GDA-stable critical points, which is a superset of local min-max solutions (strict in some cases). The connecting thread is that the behavior of these dynamics can be studied from a dynamical systems perspective.