The True Sample Complexity of Active Learning
Maria Florina Balcan
We describe a new perspective on the sample complexity of active learning. In many situations where it was generally believed that active learning does not help, we show that active learning does help in the limit, often with exponential improvements in sample complexity. These new insights arise from a subtle variation on the traditional definition of sample complexity, not previously recognized in the active learning literature.
Optimized Information Gathering using Submodular Optimization
Gaussian Process Response Surface Optimization
Response surface methods construct a Gaussian process model of an objective function based on all observed data points. The model is then used to compute which point the method should acquire next in its search for the global optimum of the objective. These optimization methods can be very efficient in terms of the number of objective function evaluations used, but existing formulations have drawbacks: Although they are intended to be "black-box," these methods are sensitive to the initial choice of function evaluations, they are not invariant to shifting and scaling of the objective function, and their experimental evaluation to date has been limited. We examine each of these issues and present rules of thumb for deploying response surface methods in practice. Along the way, we will discuss the idea of quantifying the difficulty of global optimization problems that are drawn from Gaussian process models.
Active Learning in Robotics
Robot systems have to be able to adapt their behavior and acquire new abilities. To achieve this, learning has become a crucial component of many successful robotic systems. However, data is gathered by interaction with the environment or with humans, requiring time and energy. In this talk, we will discuss some examples where active strategies reduce the amount of information/samples required to learn new models, skills or tasks. We will cover different robotic problems ranging from discovering the robot structure, learning new skills to interact with objects and imitation learning through active inverse reinforcement learning.
Playing 20 questions with the homunculus: optimal experimental design for neurophysiology
Jeremy Lewi & Liam Paninski
Neurophysiology is in many ways analogous to the game of twenty questions. One of the fundamental paradigms in experimental neuroscience is to stimulate the brain, measure the response, and then infer what the brain is doing. As in the game twenty questions, success depends critically on intelligently picking the next stimulus or question based on the data already gathered. We frame this problem in the context of neurophysiology by modeling a neuron as a generalized linear model. We present methods for constructing the stimulus which will provide the most information for deciding which GLM provides the best model of the neuron. We show that for purely spatial stimuli, we can reduce the problem to a tractable 2-d optimization which can be solved in near real time. We also consider the case of constructing near optimal stimuli when the stimulus has complex spatio-temporal structure such as a sound. We validate our methods using simulations in which the data was obtained from auditory experiments with Zebra Finch.
Large Scale Nonlinear Bayesian Experimental Design: Adaptive Compressive Sensing in the Real World
How to best acquire a real world image for nonlinear sparse reconstruction? While out of scope of current compressive sensing theory, this problem can be addressed by nonlinear sequential Bayesian experimental design, if approximate Bayesian inference is scaled up to high-resolution images by way of novel variational relaxations. We provide results of a study aiming to speed up magnetic resonance imaging by optimized undersampling, one of the most important potential applications of compressive sensing yet. In nonlinear experimental design, decisions depend on previously obtained responses, linking it to the more familiar problem of active learning. We will outline the basic properties of the former, to facilitate theory transfer with the latter. In acquisition optimization, the goal is a high-dimensional spatial signal rather than a binary label, the driving statistic is the posterior covariance matrix. Meaningful analysis must not be based on common assumptions of unstructured exact sparsity, but on weaker heavy-tails assumptions, and has to focus on approximate rather than intractable exact Bayesian inference. Recent convex variational approximations based on standard computational primitives may be promising targets towards such analyses of real practical relevance.