Universal Sequential Outlier Hypothesis Testing

Universal outlier hypothesis testing is studied in a sequential setting. Multiple observation sequences are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are generated by an "outlier" distribution, distinct from a common "typical" distribution governing the majority of the sequences. Apart from being distinct, the outlier and typical distributions can be arbitrarily close. The goal is to design a universal test to best discern all the outlier sequences. A universal test with the flavor of the repeated significance test is proposed and its asymptotic performance is characterized under various universal settings. The proposed test is shown to be universally consistent. For the model with identical outliers, the test is shown to be asymptotically optimal universally when the number of outliers is the largest possible and with the typical distribution being known, and its asymptotic performance otherwise is also characterized. An extension of the findings to the model with multiple distinct outliers is also discussed. In all cases, it is shown that the asymptotic performance guarantees for the proposed test when neither the outlier nor typical distribution is known converge to those when the typical distribution is known.Comment: Proc. of the Asilomar Conference on Signals, Systems, and Computers, 2014. To appea

Sequential Gaussian Processes for Online Learning of Nonstationary Functions

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: i) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; ii) updating a GP model sequentially is not trivial; and iii) covariance kernels often enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose an online sequential Monte Carlo algorithm to fit mixtures of GPs that capture non-stationary behavior while allowing for fast, distributed inference. By formulating hyperparameter optimization as a multi-armed bandit problem, we accelerate mixing for real time inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the context of prediction for simulated non-stationary data and hospital time series data

Lifelong Generative Modeling

Lifelong learning is the problem of learning multiple consecutive tasks in a sequential manner, where knowledge gained from previous tasks is retained and used to aid future learning over the lifetime of the learner. It is essential towards the development of intelligent machines that can adapt to their surroundings. In this work we focus on a lifelong learning approach to unsupervised generative modeling, where we continuously incorporate newly observed distributions into a learned model. We do so through a student-teacher Variational Autoencoder architecture which allows us to learn and preserve all the distributions seen so far, without the need to retain the past data nor the past models. Through the introduction of a novel cross-model regularizer, inspired by a Bayesian update rule, the student model leverages the information learned by the teacher, which acts as a probabilistic knowledge store. The regularizer reduces the effect of catastrophic interference that appears when we learn over sequences of distributions. We validate our model's performance on sequential variants of MNIST, FashionMNIST, PermutedMNIST, SVHN and Celeb-A and demonstrate that our model mitigates the effects of catastrophic interference faced by neural networks in sequential learning scenarios.Comment: 32 page