Learning how to be robust: Deep polynomial regression

Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased results when the input data is heavily contaminated by outliers. Moreover, the problem is even harder when outliers have strong structure. Departing from problem-tailored heuristics for robust estimation of parametric models, we explore deep convolutional neural networks. Our work aims to find a generic approach for training deep regression models without the explicit need of supervised annotation. We bypass the need for a tailored loss function on the regression parameters by attaching to our model a differentiable hard-wired decoder corresponding to the polynomial operation at hand. We demonstrate the value of our findings by comparing with standard robust regression methods. Furthermore, we demonstrate how to use such models for a real computer vision problem, i.e., video stabilization. The qualitative and quantitative experiments show that neural networks are able to learn robustness for general polynomial regression, with results that well overpass scores of traditional robust estimation methods.Comment: 18 pages, conferenc

PSUDOC - A Simple Diagnostic Program

This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-75-C-0643.This paper describes PSUDOC, a very simple LISP program to carry out some medical diagnosis tasks. The program's domain is a subset of clinical medicine characterized by patients presenting with edema and/or hematuria. The program's goal is to go from the presenting symptoms to a hypothesis of the underlying disease state. The program uses a variation of simple tree searching strategies called ETS.MIT Artificial Intelligence Laboratory Department of Defense Advanced Research Projects Agenc

Visible Decomposition: Real-Time Path Planning in Large Planar Environments

We describe a method called Visible Decomposition for computing collision-free paths in real time through a planar environment with a large number of obstacles. This method divides space into local visibility graphs, ensuring that all operations are local. The search time is kept low since the number of regions is proved to be small. We analyze the computational demands of the algorithm and the quality of the paths it produces. In addition, we show test results on a large simulation testbed

Learning Grammatical Models for Object Recognition

Many object recognition systems are limited by their inability to share common parts or structure among related object classes. This capability is desirable because it allows information about parts and relationships in one object class to be generalized to other classes for which it is relevant. With this goal in mind, we have designed a representation and recognition framework that captures structural variability and shared part structure within and among object classes. The framework uses probabilistic geometric grammars (PGGs) to represent object classes recursively in terms of their parts, thereby exploiting the hierarchical and substitutive structure inherent to many types of objects. To incorporate geometric and appearance information, we extend traditional probabilistic context-free grammars to represent distributions over the relative geometric characteristics of object parts as well as the appearance of primitive parts. We describe an efficient dynamic programming algorithm for object categorization and localization in images given a PGG model. We also develop an EM algorithm to estimate the parameters of a grammar structure from training data, and a search-based structure learning approach that finds a compact grammar to explain the image data while sharing substructure among classes. Finally, we describe a set of experiments that demonstrate empirically that the system provides a performance benefit

Hierarchical Task and Motion Planning in the Now

Workshop on Mobile Manipulation, IEEE International Conference on Robotics and AutomationIn this paper we outline an approach to the integration of task planning and motion planning that has the following key properties: It is aggressively hierarchical. It makes choices and commits to them in a top-down fashion in an attempt to limit the length of plans that need to be constructed, and thereby exponentially decrease the amount of search required. Importantly, our approach also limits the need to project the effect of actions into the far future. It operates on detailed, continuous geometric representations and partial symbolic descriptions. It does not require a complete symbolic representation of the input geometry or of the geometric effect of the task-level operations.This work was supported in part by the National Science Foundation under Grant No. 0712012

Finding aircraft collision-avoidance strategies using policy search methods

A progress report describing the application of policy gradient and policy search by dynamic programming methods to an aircraft collision avoidance problem inspired by the requirements of next-generation TCAS

Time-varying effects when analysing customer lifetime duration, application to the insurance market

The Cox model (Cox, 1972) is widely used in customer lifetime duration research, but it assumes that the regression coefficients are time invariant. In order to analyse the temporal covariate effects on the duration times, we propose to use an extended version of the Cox model where the parameters are allowed to vary over time. We apply this methodology to real insurance policy cancellation data and we conclude that the kind of contracts held by the customer and the concurrence of an external insurer in the cancellation influence the risk of the customer leaving the company, but the effect differs as time goes by.Cox model, customer lifetime.

Minimum Action Path theory reveals the details of stochastic biochemical transitions out of oscillatory cellular states

Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Tran- sitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible multidimensional paths, with probabilities depending non-locally on the noise. Here we characterize the escape from an oscillatory biochemical state by minimizing the Freidlin-Wentzell action, deriving from it the stochastic spiral exit path from the limit cycle. We also use the minimized action to infer the escape time probability density function