16 research outputs found
Semistochastic Quadratic Bound Methods
Partition functions arise in a variety of settings, including conditional
random fields, logistic regression, and latent gaussian models. In this paper,
we consider semistochastic quadratic bound (SQB) methods for maximum likelihood
inference based on partition function optimization. Batch methods based on the
quadratic bound were recently proposed for this class of problems, and
performed favorably in comparison to state-of-the-art techniques.
Semistochastic methods fall in between batch algorithms, which use all the
data, and stochastic gradient type methods, which use small random selections
at each iteration. We build semistochastic quadratic bound-based methods, and
prove both global convergence (to a stationary point) under very weak
assumptions, and linear convergence rate under stronger assumptions on the
objective. To make the proposed methods faster and more stable, we consider
inexact subproblem minimization and batch-size selection schemes. The efficacy
of SQB methods is demonstrated via comparison with several state-of-the-art
techniques on commonly used datasets.Comment: 11 pages, 1 figur
Convergence Rates for Inverse Problems with Impulsive Noise
We study inverse problems F(f) = g with perturbed right hand side g^{obs}
corrupted by so-called impulsive noise, i.e. noise which is concentrated on a
small subset of the domain of definition of g. It is well known that
Tikhonov-type regularization with an L^1 data fidelity term yields
significantly more accurate results than Tikhonov regularization with classical
L^2 data fidelity terms for this type of noise. The purpose of this paper is to
provide a convergence analysis explaining this remarkable difference in
accuracy. Our error estimates significantly improve previous error estimates
for Tikhonov regularization with L^1-fidelity term in the case of impulsive
noise. We present numerical results which are in good agreement with the
predictions of our analysis
Robust model training and generalisation with Studentising flows
Normalising flows are tractable probabilistic models that leverage the power
of deep learning to describe a wide parametric family of distributions, all
while remaining trainable using maximum likelihood. We discuss how these
methods can be further improved based on insights from robust (in particular,
resistant) statistics. Specifically, we propose to endow flow-based models with
fat-tailed latent distributions such as multivariate Student's , as a simple
drop-in replacement for the Gaussian distribution used by conventional
normalising flows. While robustness brings many advantages, this paper explores
two of them: 1) We describe how using fatter-tailed base distributions can give
benefits similar to gradient clipping, but without compromising the asymptotic
consistency of the method. 2) We also discuss how robust ideas lead to models
with reduced generalisation gap and improved held-out data likelihood.
Experiments on several different datasets confirm the efficacy of the proposed
approach in both regards.Comment: 9 pages, 8 figures, accepted for publication at INNF+ 2020 (Second
ICML Workshop on Invertible Neural Networks, Normalizing Flows, and Explicit
Likelihood Models