A Bayesian nonparametric approach for the analysis of multiple categorical item responses

We develop a modeling framework for joint factor and cluster analysis of datasets where multiple categorical response items are collected on a heterogeneous population of individuals. We introduce a latent factor multinomial probit model and employ prior constructions that allow inference on the number of factors as well as clustering of the subjects into homogeneous groups according to their relevant factors. Clustering, in particular, allows us to borrow strength across subjects, therefore helping in the estimation of the model parameters, particularly when the number of observations is small. We employ Markov chain Monte Carlo techniques and obtain tractable posterior inference for our objectives, including sampling of missing data. We demonstrate the effectiveness of our method on simulated data. We also analyze two real-world educational datasets and show that our method outperforms state-of-the-art methods. In the analysis of the real-world data, we uncover hidden relationships between the questions and the underlying educational concepts, while simultaneously partitioning the students into groups of similar educational mastery

Differentially Private Subspace Clustering

Subspace clustering is an unsupervised learning problem that aims at grouping data points into multiple "clusters" so that data points in a single cluster lie approximately on a low-dimensional linear subspace. It is originally motivated by 3D motion segmentation in computer vision, but has recently been generically applied to a wide range of statistical machine learning problems, which often involves sensitive datasets about human subjects. This raises a dire concern for data privacy. In this work, we build on the framework of differential privacy and present two provably private subspace clustering algorithms. We demonstrate via both theory and experiments that one of the presented methods enjoys formal privacy and utility guarantees; the other one asymptotically preserves differential privacy while having good performance in practice. Along the course of the proof, we also obtain two new provable guarantees for the agnostic subspace clustering and the graph connectivity problem which might be of independent interests

Bayesian Inference on Principal Component Analysis using Reversible Jump Markov Chain Monte Carlo

Based on the probabilistic reformulation of principal component analysis (PCA), we consider the problem of determining the number of principal components as a model selection problem. We present a hierarchical model for probabilistic PCA and construct a Bayesian inference method for this model using reversible jump Markov chain Monte Carlo (MCMC). By regarding each principal component as a point in a one-dimensional space and employing only birthdeath moves in our reversible jump methodology, our proposed method is simple and capable of automatically determining the number of principal components and estimating the parameters simultaneously under the same disciplined framework. Simulation experiments are performed to demonstrate the effectiveness of our MCMC method

Generative Models for Learning Robot Manipulation Skills from Humans

A long standing goal in artificial intelligence is to make robots seamlessly interact with humans in performing everyday manipulation skills. Learning from demonstrations or imitation learning provides a promising route to bridge this gap. In contrast to direct trajectory learning from demonstrations, many problems arise in interactive robotic applications that require higher contextual level understanding of the environment. This requires learning invariant mappings in the demonstrations that can generalize across different environmental situations such as size, position, orientation of objects, viewpoint of the observer, etc. In this thesis, we address this challenge by encapsulating invariant patterns in the demonstrations using probabilistic learning models for acquiring dexterous manipulation skills. We learn the joint probability density function of the demonstrations with a hidden semi-Markov model, and smoothly follow the generated sequence of states with a linear quadratic tracking controller. The model exploits the invariant segments (also termed as sub-goals, options or actions) in the demonstrations and adapts the movement in accordance with the external environmental situations such as size, position and orientation of the objects in the environment using a task-parameterized formulation. We incorporate high-dimensional sensory data for skill acquisition by parsimoniously representing the demonstrations using statistical subspace clustering methods and exploit the coordination patterns in latent space. To adapt the models on the fly and/or teach new manipulation skills online with the streaming data, we formulate a non-parametric scalable online sequence clustering algorithm with Bayesian non-parametric mixture models to avoid the model selection problem while ensuring tractability under small variance asymptotics. We exploit the developed generative models to perform manipulation skills with remotely operated vehicles over satellite communication in the presence of communication delays and limited bandwidth. A set of task-parameterized generative models are learned from the demonstrations of different manipulation skills provided by the teleoperator. The model captures the intention of teleoperator on one hand and provides assistance in performing remote manipulation tasks on the other hand under varying environmental situations. The assistance is formulated under time-independent shared control, where the model continuously corrects the remote arm movement based on the current state of the teleoperator; and/or time-dependent autonomous control, where the model synthesizes the movement of the remote arm for autonomous skill execution. Using the proposed methodology with the two-armed Baxter robot as a mock-up for semi-autonomous teleoperation, we are able to learn manipulation skills such as opening a valve, pick-and-place an object by obstacle avoidance, hot-stabbing (a specialized underwater task akin to peg-in-a-hole task), screw-driver target snapping, and tracking a carabiner in as few as 4 - 8 demonstrations. Our study shows that the proposed manipulation assistance formulations improve the performance of the teleoperator by reducing the task errors and the execution time, while catering for the environmental differences in performing remote manipulation tasks with limited bandwidth and communication delays