44,946 research outputs found
Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments
This paper considers uniformly valid (over a class of data generating
processes) inference for linear functionals of partially identified parameters
in cases where the identified set is defined by linear (in the parameter)
moment inequalities. We propose a bootstrap procedure for constructing
uniformly valid confidence sets for a linear functional of a partially
identified parameter. The proposed method amounts to bootstrapping the value
functions of a linear optimization problem, and subsumes subvector inference as
a special case. In other words, this paper shows the conditions under which
``naively'' bootstrapping a linear program can be used to construct a
confidence set with uniform correct coverage for a partially identified linear
functional. Unlike other proposed subvector inference procedures, our procedure
does not require the researcher to repeatedly invert a hypothesis test, and is
extremely computationally efficient. In addition to the new procedure, the
paper also discusses connections between the literature on optimization and the
literature on subvector inference in partially identified models
Sampling-Based Methods for Factored Task and Motion Planning
This paper presents a general-purpose formulation of a large class of
discrete-time planning problems, with hybrid state and control-spaces, as
factored transition systems. Factoring allows state transitions to be described
as the intersection of several constraints each affecting a subset of the state
and control variables. Robotic manipulation problems with many movable objects
involve constraints that only affect several variables at a time and therefore
exhibit large amounts of factoring. We develop a theoretical framework for
solving factored transition systems with sampling-based algorithms. The
framework characterizes conditions on the submanifold in which solutions lie,
leading to a characterization of robust feasibility that incorporates
dimensionality-reducing constraints. It then connects those conditions to
corresponding conditional samplers that can be composed to produce values on
this submanifold. We present two domain-independent, probabilistically complete
planning algorithms that take, as input, a set of conditional samplers. We
demonstrate the empirical efficiency of these algorithms on a set of
challenging task and motion planning problems involving picking, placing, and
pushing
On the Optimality of a Class of LP-based Algorithms
In this paper we will be concerned with a class of packing and covering
problems which includes Vertex Cover and Independent Set. Typically, one can
write an LP relaxation and then round the solution. In this paper, we explain
why the simple LP-based rounding algorithm for the \\VC problem is optimal
assuming the UGC. Complementing Raghavendra's result, our result generalizes to
a class of strict, covering/packing type CSPs
Hypothesis Testing For Network Data in Functional Neuroimaging
In recent years, it has become common practice in neuroscience to use
networks to summarize relational information in a set of measurements,
typically assumed to be reflective of either functional or structural
relationships between regions of interest in the brain. One of the most basic
tasks of interest in the analysis of such data is the testing of hypotheses, in
answer to questions such as "Is there a difference between the networks of
these two groups of subjects?" In the classical setting, where the unit of
interest is a scalar or a vector, such questions are answered through the use
of familiar two-sample testing strategies. Networks, however, are not Euclidean
objects, and hence classical methods do not directly apply. We address this
challenge by drawing on concepts and techniques from geometry, and
high-dimensional statistical inference. Our work is based on a precise
geometric characterization of the space of graph Laplacian matrices and a
nonparametric notion of averaging due to Fr\'echet. We motivate and illustrate
our resulting methodologies for testing in the context of networks derived from
functional neuroimaging data on human subjects from the 1000 Functional
Connectomes Project. In particular, we show that this global test is more
statistical powerful, than a mass-univariate approach. In addition, we have
also provided a method for visualizing the individual contribution of each edge
to the overall test statistic.Comment: 34 pages. 5 figure
Doubly autoparallel structure on the probability simplex
On the probability simplex, we can consider the standard information
geometric structure with the e- and m-affine connections mutually dual with
respect to the Fisher metric. The geometry naturally defines submanifolds
simultaneously autoparallel for the both affine connections, which we call {\em
doubly autoparallel submanifolds}.
In this note we discuss their several interesting common properties. Further,
we algebraically characterize doubly autoparallel submanifolds on the
probability simplex and give their classification
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