The Automatic Statistician: A Relational Perspective

Department of Computer EngineeringGaussian Processes (GPs) provide a general and analytically tractable way of capturing complex time-varying, nonparametric functions. The time varying parameters of GPs can be explained as a composition of base kernels such as linear, smoothness or periodicity in that covariance kernels are closed under addition and multiplication. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GPs. Unfortunately, learning a composite covariance kernel with a single time-series dataset often results in less informative kernels instead of finding qualitative distinct descriptions. We address this issue by proposing a relational kernel learning which can model relationship between sets of data and find shared structure among the time series datasets. We show the shared structure can help learning more accurate models for sets of regression problems with some synthetic data, US top market capitalization stock data and US house sales index data.ope

Automatic Construction of Nonparametric Relational Regression Models for Multiple Time Series

Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown time-series data nonparametrically using GP with a composite covariance kernel function. Unfortunately, learning a composite covariance kernel with a single time-series data set often results in less informative kernel that may not give qualitative, distinctive descriptions of data. We address this challenge by proposing two relational kernel learning methods which can model multiple time-series data sets by finding common, shared causes of changes. We show that the relational kernel learning methods find more accurate models for regression problems on several real-world data sets; US stock data, US house price index data and currency exchange rate data

A Deterministic Partition Function Approximation for Exponential Random Graph Models

Exponential Random Graphs Models (ERGM) are common, simple statistical models for social network and other network structures. Unfortunately, inference and learning with them is hard even for small networks because their partition functions are intractable for precise computation. In this paper, we introduce a new quadratic time deterministic approximation to these partition functions. Our main insight enabling this advance is that subgraph statistics is sufficient to derive a lower bound for partition functions given that the model is not dominated by a few graphs. The proposed method differs from existing methods in its ways of exploiting asymptotic properties of subgraph statistics. Compared to the current Monte Carlo simulation based methods, the new method is scalable, stable, and precise enough for inference tasks

Automatic Construction of Nonparametric Relational Regression Models for Multiple Time Series

Abstract Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of time-series data by treating unknown timeseries data nonparametrically using GP with a composite covariance kernel function. Unfortunately, learning a composite covariance kernel with a single time-series data set often results in less informative kernel that may not give qualitative, distinctive descriptions of data. We address this challenge by proposing two relational kernel learning methods which can model multiple time-series data sets by finding common, shared causes of changes. We show that the relational kernel learning methods find more accurate models for regression problems on several real-world data sets; US stock data, US house price index data and currency exchange rate data