arXiv subjects

Priyank Jaini

Publications and source records attributed to Priyank Jaini.

21 records · Page 2Linked to original sources

arXiv2020

Tails of Lipschitz Triangular Flows

We investigate the ability of popular flow based methods to capture tail-properties of a target density by studying the increasing triangular maps used in these flow methods acting on a tractable source density. We show that the density quantile functions of the source and target density provide a precise characterization of the slope of transformation required to capture tails in a target density. We further show that any Lipschitz-continuous transport map acting on a source density will result in a density with similar tail properties as the source, highlighting the trade-off between a complex source density and a sufficiently expressive transformation to capture desirable properties of a target density. Subsequently, we illustrate that flow models like Real-NVP, MAF, and Glow as implemented originally lack the ability to capture a distribution with non-Gaussian tails. We circumvent this problem by proposing tail-adaptive flows consisting of a source distribution that can be learned simultaneously with the triangular map to capture tail-properties of a target density. We perform several synthetic and real-world experiments to compliment our theoretical findings.

math.ST↗

arXiv2019

Sum-of-Squares Polynomial Flow

Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional density estimation, by specifying one-dimensional transformations (equivalently conditional densities) and appropriate conditioner networks. This framework (a) reveals the commonalities and differences of existing autoregressive and flow based methods, (b) allows a unified understanding of the limitations and representation power of these recent approaches and, (c) motivates us to uncover a new Sum-of-Squares (SOS) flow that is interpretable, universal, and easy to train. We perform several synthetic experiments on various density geometries to demonstrate the benefits (and short-comings) of such transformations. SOS flows achieve competitive results in simulations and several real-world datasets.

cs.LG↗

arXiv2016

Online and Distributed learning of Gaussian mixture models by Bayesian Moment Matching

The Gaussian mixture model is a classic technique for clustering and data modeling that is used in numerous applications. With the rise of big data, there is a need for parameter estimation techniques that can handle streaming data and distribute the computation over several processors. While online variants of the Expectation Maximization (EM) algorithm exist, their data efficiency is reduced by a stochastic approximation of the E-step and it is not clear how to distribute the computation over multiple processors. We propose a Bayesian learning technique that lends itself naturally to online and distributed computation. Since the Bayesian posterior is not tractable, we project it onto a family of tractable distributions after each observation by matching a set of sufficient moments. This Bayesian moment matching technique compares favorably to online EM in terms of time and accuracy on a set of data modeling benchmarks.

cs.AI↗