In active learning, sampling bias could pose a serious inconsistency problem and hinder the algorithm from finding the optimal hypothesis. However, many methods for neural networks are hypothesis space agnostic and do not address this problem. We examine active learning with convolutional neural networks through the principled lens of version space reduction. We identify the connection between two approaches---prior mass reduction and diameter reduction---and propose a new diameter-based querying method---the minimum Gibbs-vote disagreement. By estimating version space diameter and bias, we illustrate how version space of neural networks evolves and examine the realizability assumption. With experiments on MNIST, Fashion-MNIST, SVHN and STL-10 datasets, we demonstrate that diameter reduction methods reduce the version space more effectively and perform better than prior mass reduction and other baselines, and that the Gibbs vote disagreement is on par with the best query method.

We study constrained online convex optimization, where the constraints consist of a relatively simple constraint set (e.g. a Euclidean ball) and multiple functional constraints. Projections onto such decision sets are usually computationally challenging. So instead of enforcing all constraints over each slot, we allow decisions to violate these functional constraints but aim at achieving a low regret and a low cumulative constraint violation over a horizon of $T$ time slot. The best known bound for solving this problem is $\mathcal{O}(\sqrt{T})$ regret and $\mathcal{O}(1)$ constraint violation, whose algorithms and analysis are restricted to Euclidean spaces. In this paper, we propose a new online primal-dual mirror prox algorithm whose regret is measured via a total gradient variation $V_*(T)$ over a sequence of $T$ loss functions. Specifically, we show that the proposed algorithm can achieve an $\mathcal{O}(\sqrt{V_*(T)})$ regret and $\mathcal{O}(1)$ constraint violation simultaneously. Such a bound holds in general non-Euclidean spaces, is never worse than the previously known $\big( \mathcal{O}(\sqrt{T}), \mathcal{O}(1) \big)$ result, and can be much better on regret when the variation is small. Furthermore, our algorithm is computationally efficient in that only two mirror descent steps are required during each slot instead of solving a general Lagrangian minimization problem. Along the way, our bounds also improve upon those of previous attempts using mirror-prox-type algorithms solving this problem, which yield a relatively worse $\mathcal{O}(T^{2/3})$ regret and $\mathcal{O}(T^{2/3})$ constraint violation.

We analyze the optimization landscape of a recently introduced tunable class of loss functions called $\alpha$-loss, $\alpha \in (0,\infty]$, in the logistic model. This family encapsulates the exponential loss ($\alpha = 1/2$), the log-loss ($\alpha = 1$), and the 0-1 loss ($\alpha = \infty$) and contains compelling properties that enable the practitioner to discern among a host of operating conditions relevant to emerging learning methods. Specifically, we study the evolution of the optimization landscape of $\alpha$-loss with respect to $\alpha$ using tools drawn from the study of strictly-locally-quasi-convex functions in addition to geometric techniques. We interpret these results in terms of optimization complexity via normalized gradient descent.

Non-negative Matrix Factorization (NMF) has proven to be a powerful unsupervised learning method for uncovering hidden features in complex and noisy data sets with applications in data mining, text recognition, dimension reduction, face recognition, anomaly detection, blind source separation, and many other fields. An important input for NMF is the latent dimensionality of the data, that is, the number of hidden features, K, present in the explored data set. Unfortunately, this quantity is rarely known a priori. We utilize a supervised machine learning approach in combination with a recent method for model determination, called NMFk, to determine the number of hidden features automatically. NMFk performs a set of NMF simulations on an ensemble of matrices, obtained by bootstrapping the initial data set, and determines which K produces stable groups of latent features that reconstruct the initial data set well. We then train a Multi-Layer Perceptron (MLP) classifier network to determine the correct number of latent features utilizing the statistics and characteristics of the NMF solutions, obtained from NMFk. In order to train the MLP classifier, a training set of 58,660 matrices with predetermined latent features were factorized with NMFk. The MLP classifier in conjunction with NMFk maintains a greater than 95% success rate when applied to a held out test set. Additionally, when applied to two well-known benchmark data sets, the swimmer and MIT face data, NMFk/MLP correctly recovered the established number of hidden features. Finally, we compared the accuracy of our method to the ARD, AIC and Stability-based methods.

Beyond the possible misuses of technology, there is an increased awareness that these processes are not neutral and can reproduce and amplify past and current structural inequalities [1, 2]. Within this context, particular interest is paid to the role of machine learning (ML) with well known examples of models biased against historically discriminated groups [3, 4, 5] or the intersection of these groups [6, 7]. Fairness in ML has emerged as a community initially motivated to develop technological solutions to the disparate impact and treatment by biased algorithms [8, 9, 10, 11, 5] that also moves to a broader and multi-disciplinary understanding of the issues of socio-technological interventions [12, 13, 14, 15]. This work contribute to this field by studying how far bias mitigation can go whilst satisfying the accuracy and transparency of the models, thus providing a tool for a wider understanding of the technological boundaries of socio-technical proposals. Bias mitigation techniques can broadly be divided into three non-exclusive categories [16]: (1) preprocessing, (2) inprocessing, and (3) postprocessing. The preprocessing techniques attempt to learn new representations of data to satisfy fairness definitions. The inprocessing methods involve modifying the classifier algorithm by adding a fairness constraint to the optimization problem. The postprocessing methods aim at removing discriminatory decisions after the model is trained. Normally, in inprocessing approaches the fairness criteria are used as an optimization constraint rather than as a guide to build a more equitable prediction model.

Lipschitz bandits is a prominent version of multi-armed bandits that studies large, structured action spaces such as the [0,1] interval, where similar actions are guaranteed to have similar rewards. A central theme here is the adaptive discretization of the action space, which gradually "zooms in" on the more promising regions thereof. The goal is to take advantage of "nicer" problem instances, while retaining near-optimal worst-case performance. While the stochastic version of the problem is well-understood, the general version with adversarially chosen rewards is not. We provide the first algorithm for adaptive discretization in the adversarial version, and derive instance-dependent regret bounds. In particular, we recover the worst-case optimal regret bound for the adversarial version, and the instance-dependent regret bound for the stochastic version. Further, an application of our algorithm to dynamic pricing (a version in which the algorithm repeatedly adjusts prices for a product) enjoys these regret bounds without any smoothness assumptions.

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms can have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior uncertainty. And, even if the most important modes can be found, it is difficult to evaluate their relative weights in the posterior. Here we propose an alternative approach, using parallel runs of MCMC, variational, or mode-based inference to hit as many modes or separated regions as possible, and then combining these using importance sampling based Bayesian stacking, a scalable method for constructing a weighted average of distributions so as to maximize cross-validated prediction utility. The result from stacking is not necessarily equivalent, even asymptotically, to fully Bayesian inference, but it serves many of the same goals. Under misspecified models, stacking can give better predictive performance than full Bayesian inference, hence the multimodality can be considered a blessing rather than a curse. We explore with an example where the stacked inference approximates the true data generating process from the misspecified model, an example of inconsistent inference, and non-mixing samplers. We elaborate the practical implantation in the context of latent Dirichlet allocation, Gaussian process regression, hierarchical model, variational inference in horseshoe regression, and neural networks.

Empowered by expressive function approximators such as neural networks, deep reinforcement learning (DRL) achieves tremendous empirical successes. However, learning expressive function approximators requires collecting a large dataset (interventional data) by interacting with the environment. Such a lack of sample efficiency prohibits the application of DRL to critical scenarios, e.g., autonomous driving and personalized medicine, since trial and error in the online setting is often unsafe and even unethical. In this paper, we study how to incorporate the dataset (observational data) collected offline, which is often abundantly available in practice, to improve the sample efficiency in the online setting. To incorporate the possibly confounded observational data, we propose the deconfounded optimistic value iteration (DOVI) algorithm, which incorporates the confounded observational data in a provably efficient manner. More specifically, DOVI explicitly adjusts for the confounding bias in the observational data, where the confounders are partially observed or unobserved. In both cases, such adjustments allow us to construct the bonus based on a notion of information gain, which takes into account the amount of information acquired from the offline setting. In particular, we prove that the regret of DOVI is smaller than the optimal regret achievable in the pure online setting by a multiplicative factor, which decreases towards zero when the confounded observational data are more informative upon the adjustments. Our algorithm and analysis serve as a step towards causal reinforcement learning.

We analyze the convergence of the averaged stochastic gradient descent for over-parameterized two-layer neural networks for regression problems. It was recently found that, under the neural tangent kernel (NTK) regime, where the learning dynamics for overparameterized neural networks can be mostly characterized by that for the associated reproducing kernel Hilbert space (RKHS), an NTK plays an important role in revealing the global convergence of gradient-based methods. However, there is still room for a convergence rate analysis in the NTK regime. In this study, we show the global convergence of the averaged stochastic gradient descent and derive the optimal convergence rate by exploiting the complexities of the target function and the RKHS associated with the NTK. Moreover, we show that the target function specified by the NTK of a ReLU network can be learned at the optimal convergence rate through a smooth approximation of ReLU networks under certain conditions.

Graph convolution operator of the GCN model is originally motivated from a localized first-order approximation of spectral graph convolutions.This work stands on a different view; establishing a connection between graph convolution and graph-regularized PCA. Based on this connection, GCN architecture, shaped by stacking graph convolution layers, shares a close relationship with stacking graph-regularized PCA (GPCA). We empirically demonstrate that the unsupervised embeddings by GPCA paired with a logistic regression classifier achieves similar performance to GCN on semi-supervised node classification tasks. Further, we capitalize on the discovered relationship to design an effective initialization strategy for GCN based on stacking GPCA.