Non-Gaussian Geostatistical Modeling using (skew) t Processes

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew-Gaussian process, thus obtaining a process with skew-t marginal distributions. For the proposed (skew) $t$ process we study the second-order and geometrical properties and in the $t$ case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the $t$ process. Moreover we compare the performance of the optimal linear predictor of the $t$ process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australi

Robust density modelling using the student's t-distribution for human action recognition

The extraction of human features from videos is often inaccurate and prone to outliers. Such outliers can severely affect density modelling when the Gaussian distribution is used as the model since it is highly sensitive to outliers. The Gaussian distribution is also often used as base component of graphical models for recognising human actions in the videos (hidden Markov model and others) and the presence of outliers can significantly affect the recognition accuracy. In contrast, the Student's t-distribution is more robust to outliers and can be exploited to improve the recognition rate in the presence of abnormal data. In this paper, we present an HMM which uses mixtures of t-distributions as observation probabilities and show how experiments over two well-known datasets (Weizmann, MuHAVi) reported a remarkable improvement in classification accuracy. © 2011 IEEE

Latent variable models for understanding user behavior in software applications

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 147-157).Understanding user behavior in software applications is of significant interest to software developers and companies. By having a better understanding of the user needs and usage patterns, the developers can design a more efficient workflow, add new features, or even automate the user's workflow. In this thesis, I propose novel latent variable models to understand, predict and eventually automate the user interaction with a software application. I start by analyzing users' clicks using time series models; I introduce models and inference algorithms for time series segmentation which are scalable to large-scale user datasets. Next, using a conditional variational autoencoder and some related models, I introduce a framework for automating the user interaction with a software application. I focus on photo enhancement applications, but this framework can be applied to any domain where segmentation, prediction and personalization is valuable. Finally, by combining sequential Monte Carlo and variational inference, I propose a new inference scheme which has better convergence properties than other reasonable baselines.by Ardavan Saeedi.Ph. D