How well can we estimate the probability that the classification, $C(f(x))$, predicted by a deep neural network is correct (or in the Top 5)? We consider the case of a classification neural network trained with the KL divergence which is assumed to generalize, as measured empirically by the test error and test loss. We present conditional probabilities for predictions based on the histogram of uncertainty metrics, which have a significant Bayes ratio. Previous work in this area includes Bayesian neural networks. Our metric is twice as predictive, based on the expected Bayes ratio, on ImageNet compared to our best tuned implementation of Bayesian dropout~\cite{gal2016dropout}. Our method uses just the softmax values and a stored histogram so it is essentially free to compute, compared to many times inference cost for Bayesian dropout.

We propose a new online algorithm for minimizing the cumulative regret in stochastic linear bandits. The key idea is to build a perturbed history, which mixes the history of observed rewards with a pseudo-history of randomly generated i.i.d. pseudo-rewards. Our algorithm, perturbed-history exploration in a linear bandit (LinPHE), estimates a linear model from its perturbed history and pulls the arm with the highest value under that model. We prove a $\tilde{O}(d \sqrt{n})$ gap-free bound on the expected $n$-round regret of LinPHE, where $d$ is the number of features. Our analysis relies on novel concentration and anti-concentration bounds on the weighted sum of Bernoulli random variables. To show the generality of our design, we extend LinPHE to a logistic reward model. We evaluate both algorithms empirically and show that they are practical.

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalman filter gain, given a single trajectory of output measurements over a finite horizon of length $N$. Based on a subspace identification algorithm and a finite number of $N$ output samples, we provide non-asymptotic high-probability upper bounds for the system parameter estimation errors. Our analysis uses recent results from random matrix theory, self-normalized martingales and SVD robustness, in order to show that with high probability the estimation errors decrease with a rate of $1/\sqrt{N}$. Our non-asymptotic bounds not only agree with classical asymptotic results, but are also valid even when the system is marginally stable.

Multitask learning aims at solving a set of related tasks simultaneously, by exploiting the shared knowledge for improving the performance on individual tasks. Hence, an important aspect of multitask learning is to understand the similarities within a set of tasks. Previous works have incorporated this similarity information explicitly (e.g., weighted loss for each task) or implicitly (e.g., adversarial loss for feature adaptation), for achieving good empirical performances. However, the theoretical motivations for adding task similarity knowledge are often missing or incomplete. In this paper, we give a different perspective from a theoretical point of view to understand this practice. We first provide an upper bound on the generalization error of multitask learning, showing the benefit of explicit and implicit task similarity knowledge. We systematically derive the bounds based on two distinct task similarity metrics: H divergence and Wasserstein distance. From these theoretical results, we revisit the Adversarial Multi-task Neural Network, proposing a new training algorithm to learn the task relation coefficients and neural network parameters iteratively. We assess our new algorithm empirically on several benchmarks, showing not only that we find interesting and robust task relations, but that the proposed approach outperforms the baselines, reaffirming the benefits of theoretical insight in algorithm design.

We augment linear Support Vector Machine (SVM) classifiers by adding three important features: (i) we introduce a regularization constraint to induce a sparse classifier; (ii) we devise a method that partitions the positive class into clusters and selects a sparse SVM classifier for each cluster; and (iii) we develop a method to optimize the values of controllable variables in order to reduce the number of data points which are predicted to have an undesirable outcome, which, in our setting, coincides with being in the positive class. The latter feature leads to personalized prescriptions/recommendations. We apply our methods to the problem of predicting and preventing hospital readmissions within 30-days from discharge for patients that underwent a general surgical procedure. To that end, we leverage a large dataset containing over 2.28 million patients who had surgeries in the period 2011--2014 in the U.S. The dataset has been collected as part of the American College of Surgeons National Surgical Quality Improvement Program (NSQIP).

The goal of this paper is to deal with a data scarcity scenario where deep learning techniques use to fail. We compare the use of two well established techniques, Restricted Boltzmann Machines and Variational Auto-encoders, as generative models in order to increase the training set in a classification framework. Essentially, we rely on Markov Chain Monte Carlo (MCMC) algorithms for generating new samples. We show that generalization can be improved comparing this methodology to other state-of-the-art techniques, e.g. semi-supervised learning with ladder networks. Furthermore, we show that RBM is better than VAE generating new samples for training a classifier with good generalization capabilities.

High dimensional data often contain multiple facets, and several clustering patterns (views) can co-exist under different feature subspaces. While multi-view clustering algorithms were proposed, the uncertainty quantification remains difficult --- a particular challenge is in the high complexity of estimating the cluster assignment probability under each view, or/and to efficiently share information across views. In this article, we propose an empirical Bayes approach --- viewing the similarity matrices generated over subspaces as rough first-stage estimates for co-assignment probabilities, in its Kullback-Leibler neighborhood we obtain a refined low-rank soft cluster graph, formed by the pairwise product of simplex coordinates. Interestingly, each simplex coordinate directly encodes the cluster assignment uncertainty. For multi-view clustering, we equip each similarity matrix with a mixed membership over a small number of latent views, leading to effective dimension reduction. With a high model flexibility, the estimation can be succinctly re-parameterized as a continuous optimization problem, hence enjoys gradient-based computation. Theory establishes the connection of this model to random cluster graph under multiple views. Compared to single-view clustering approaches, substantially more interpretable results are obtained when clustering brains from human traumatic brain injury study, using high-dimensional gene expression data. KEY WORDS: Co-regularized Clustering, Consensus, PAC-Bayes, Random Cluster Graph, Variable Selection

This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple subjects. When approached from a bayesian perspective, such mixed-effects models typically rely upon a hierarchical generative model of the data, whereby both within- and between-subject effects contribute to the overall observed variance. The ensuing VB scheme can be used to assess statistical significance at the group level and/or to capture inter-individual differences. Alternatively, it can be seen as an adaptive regularization procedure, which iteratively learns the corresponding within-subject priors from estimates of the group distribution of effects of interest (cf. so-called "empirical bayes" approaches). We outline the mathematical derivation of the ensuing VB scheme, whose open-source implementation is available as part the VBA toolbox.

A detailed understanding of wind turbine performance status classification can improve operations and maintenance in the wind energy industry. Due to different engineering properties of wind turbines, the standard supervised learning models used for classification do not generalize across data sets obtained from different wind sites. We propose two methods to deal with the transferability of the trained models: first, data normalization in the form of power curve alignment, and second, a robust method based on convolutional neural networks and feature-space extension. We demonstrate the success of our methods on real-world data sets with industrial applications. Keywords: Machine learning, classification, generalization, CNN, wind turbine, wind energy 1. Introduction Classification of operational status is an important step for performance analysis of wind farms from data of SCADA (Supervisory Control and Data Acquisition) type.

The Binary Space Partitioning~(BSP)-Tree process is proposed to produce flexible 2-D partition structures which are originally used as a Bayesian nonparametric prior for relational modelling. It can hardly be applied to other learning tasks such as regression trees because extending the BSP-Tree process to a higher dimensional space is nontrivial. This paper is the first attempt to extend the BSP-Tree process to a d-dimensional (d>2) space. We propose to generate a cutting hyperplane, which is assumed to be parallel to d-2 dimensions, to cut each node in the d-dimensional BSP-tree. By designing a subtle strategy to sample two free dimensions from d dimensions, the extended BSP-Tree process can inherit the essential self-consistency property from the original version. Based on the extended BSP-Tree process, an ensemble model, which is named the BSP-Forest, is further developed for regression tasks. Thanks to the retained self-consistency property, we can thus significantly reduce the geometric calculations in the inference stage. Compared to its counterpart, the Mondrian Forest, the BSP-Forest can achieve similar performance with fewer cuts due to its flexibility. The BSP-Forest also outperforms other (Bayesian) regression forests on a number of real-world data sets.