Asymptotic Analysis of Generative Semi-Supervised Learning

Semisupervised learning has emerged as a popular framework for improving modeling accuracy while controlling labeling cost. Based on an extension of stochastic composite likelihood we quantify the asymptotic accuracy of generative semi-supervised learning. In doing so, we complement distribution-free analysis by providing an alternative framework to measure the value associated with different labeling policies and resolve the fundamental question of how much data to label and in what manner. We demonstrate our approach with both simulation studies and real world experiments using naive Bayes for text classification and MRFs and CRFs for structured prediction in NLP.Comment: 12 pages, 9 figure

Accuracy of Latent-Variable Estimation in Bayesian Semi-Supervised Learning

Hierarchical probabilistic models, such as Gaussian mixture models, are widely used for unsupervised learning tasks. These models consist of observable and latent variables, which represent the observable data and the underlying data-generation process, respectively. Unsupervised learning tasks, such as cluster analysis, are regarded as estimations of latent variables based on the observable ones. The estimation of latent variables in semi-supervised learning, where some labels are observed, will be more precise than that in unsupervised, and one of the concerns is to clarify the effect of the labeled data. However, there has not been sufficient theoretical analysis of the accuracy of the estimation of latent variables. In a previous study, a distribution-based error function was formulated, and its asymptotic form was calculated for unsupervised learning with generative models. It has been shown that, for the estimation of latent variables, the Bayes method is more accurate than the maximum-likelihood method. The present paper reveals the asymptotic forms of the error function in Bayesian semi-supervised learning for both discriminative and generative models. The results show that the generative model, which uses all of the given data, performs better when the model is well specified.Comment: 25 pages, 4 figure

Model Selection for Stochastic Block Models

As a flexible representation for complex systems, networks (graphs) model entities and their interactions as nodes and edges. In many real-world networks, nodes divide naturally into functional communities, where nodes in the same group connect to the rest of the network in similar ways. Discovering such communities is an important part of modeling networks, as community structure offers clues to the processes which generated the graph. The stochastic block model is a popular network model based on community structures. It splits nodes into blocks, within which all nodes are stochastically equivalent in terms of how they connect to the rest of the network. As a generative model, it has a well-defined likelihood function with consistent parameter estimates. It is also highly flexible, capable of modeling a wide variety of community structures, including degree specific and overlapping communities. Performance of different block models vary under different scenarios. Picking the right model is crucial for successful network modeling. A good model choice should balance the trade-off between complexity and fit. The task of model selection is to automatically choose such a model given the data and the inference task. As a problem of wide interest, numerous statistical model selection techniques have been developed for classic independent data. Unfortunately, it has been a common mistake to use these techniques in block models without rigorous examinations of their derivations, ignoring the fact that some of the fundamental assumptions has been violated by moving into the domain of relational data sets such as networks. In this dissertation, I thoroughly exam the literature of statistical model selection techniques, including both Frequentist and Bayesian approaches. My goal is to develop principled statistical model selection criteria for block models by adapting classic methods for network data. I do this by running bootstrapping simulations with an efficient algorithm, and correcting classic model selection theories for block models based on the simulation data. The new model selection methods are verified by both synthetic and real world data sets

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