164,320 research outputs found
Data-Driven Estimation in Equilibrium Using Inverse Optimization
Equilibrium modeling is common in a variety of fields such as game theory and
transportation science. The inputs for these models, however, are often
difficult to estimate, while their outputs, i.e., the equilibria they are meant
to describe, are often directly observable. By combining ideas from inverse
optimization with the theory of variational inequalities, we develop an
efficient, data-driven technique for estimating the parameters of these models
from observed equilibria. We use this technique to estimate the utility
functions of players in a game from their observed actions and to estimate the
congestion function on a road network from traffic count data. A distinguishing
feature of our approach is that it supports both parametric and
\emph{nonparametric} estimation by leveraging ideas from statistical learning
(kernel methods and regularization operators). In computational experiments
involving Nash and Wardrop equilibria in a nonparametric setting, we find that
a) we effectively estimate the unknown demand or congestion function,
respectively, and b) our proposed regularization technique substantially
improves the out-of-sample performance of our estimators.Comment: 36 pages, 5 figures Additional theorems for generalization guarantees
and statistical analysis adde
A Geometric Approach to Sound Source Localization from Time-Delay Estimates
This paper addresses the problem of sound-source localization from time-delay
estimates using arbitrarily-shaped non-coplanar microphone arrays. A novel
geometric formulation is proposed, together with a thorough algebraic analysis
and a global optimization solver. The proposed model is thoroughly described
and evaluated. The geometric analysis, stemming from the direct acoustic
propagation model, leads to necessary and sufficient conditions for a set of
time delays to correspond to a unique position in the source space. Such sets
of time delays are referred to as feasible sets. We formally prove that every
feasible set corresponds to exactly one position in the source space, whose
value can be recovered using a closed-form localization mapping. Therefore we
seek for the optimal feasible set of time delays given, as input, the received
microphone signals. This time delay estimation problem is naturally cast into a
programming task, constrained by the feasibility conditions derived from the
geometric analysis. A global branch-and-bound optimization technique is
proposed to solve the problem at hand, hence estimating the best set of
feasible time delays and, subsequently, localizing the sound source. Extensive
experiments with both simulated and real data are reported; we compare our
methodology to four state-of-the-art techniques. This comparison clearly shows
that the proposed method combined with the branch-and-bound algorithm
outperforms existing methods. These in-depth geometric understanding, practical
algorithms, and encouraging results, open several opportunities for future
work.Comment: 13 pages, 2 figures, 3 table, journa
Almost-Smooth Histograms and Sliding-Window Graph Algorithms
We study algorithms for the sliding-window model, an important variant of the
data-stream model, in which the goal is to compute some function of a
fixed-length suffix of the stream. We extend the smooth-histogram framework of
Braverman and Ostrovsky (FOCS 2007) to almost-smooth functions, which includes
all subadditive functions. Specifically, we show that if a subadditive function
can be -approximated in the insertion-only streaming model, then
it can be -approximated also in the sliding-window model with
space complexity larger by factor , where is the
window size.
We demonstrate how our framework yields new approximation algorithms with
relatively little effort for a variety of problems that do not admit the
smooth-histogram technique. For example, in the frequency-vector model, a
symmetric norm is subadditive and thus we obtain a sliding-window
-approximation algorithm for it. Another example is for streaming
matrices, where we derive a new sliding-window
-approximation algorithm for Schatten -norm. We then
consider graph streams and show that many graph problems are subadditive,
including maximum submodular matching, minimum vertex-cover, and maximum
-cover, thereby deriving sliding-window -approximation algorithms for
them almost for free (using known insertion-only algorithms). Finally, we
design for every an artificial function, based on the
maximum-matching size, whose almost-smoothness parameter is exactly
Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor
We estimate the distribution of random parameters in a distributed parameter
model with unbounded input and output for the transdermal transport of ethanol
in humans. The model takes the form of a diffusion equation with the input
being the blood alcohol concentration and the output being the transdermal
alcohol concentration. Our approach is based on the idea of reformulating the
underlying dynamical system in such a way that the random parameters are now
treated as additional space variables. When the distribution to be estimated is
assumed to be defined in terms of a joint density, estimating the distribution
is equivalent to estimating the diffusivity in a multi-dimensional diffusion
equation and thus well-established finite dimensional approximation schemes,
functional analytic based convergence arguments, optimization techniques, and
computational methods may all be employed. We use our technique to estimate a
bivariate normal distribution based on data for multiple drinking episodes from
a single subject.Comment: 10 page
The Kalai-Smorodinski solution for many-objective Bayesian optimization
An ongoing aim of research in multiobjective Bayesian optimization is to
extend its applicability to a large number of objectives. While coping with a
limited budget of evaluations, recovering the set of optimal compromise
solutions generally requires numerous observations and is less interpretable
since this set tends to grow larger with the number of objectives. We thus
propose to focus on a specific solution originating from game theory, the
Kalai-Smorodinsky solution, which possesses attractive properties. In
particular, it ensures equal marginal gains over all objectives. We further
make it insensitive to a monotonic transformation of the objectives by
considering the objectives in the copula space. A novel tailored algorithm is
proposed to search for the solution, in the form of a Bayesian optimization
algorithm: sequential sampling decisions are made based on acquisition
functions that derive from an instrumental Gaussian process prior. Our approach
is tested on four problems with respectively four, six, eight, and nine
objectives. The method is available in the Rpackage GPGame available on CRAN at
https://cran.r-project.org/package=GPGame
Optimal Precoders for Tracking the AoD and AoA of a mm-Wave Path
In millimeter-wave channels, most of the received energy is carried by a few
paths. Traditional precoders sweep the angle-of-departure (AoD) and
angle-of-arrival (AoA) space with directional precoders to identify directions
with largest power. Such precoders are heuristic and lead to sub-optimal
AoD/AoA estimation. We derive optimal precoders, minimizing the Cram\'{e}r-Rao
bound (CRB) of the AoD/AoA, assuming a fully digital architecture at the
transmitter and spatial filtering of a single path. The precoders are found by
solving a suitable convex optimization problem. We demonstrate that the
accuracy can be improved by at least a factor of two over traditional
precoders, and show that there is an optimal number of distinct precoders
beyond which the CRB does not improve.Comment: Resubmission to IEEE Trans. on Signal Processing. 12 pages and 9
figure
Optimal Data Acquisition for Statistical Estimation
We consider a data analyst's problem of purchasing data from strategic agents
to compute an unbiased estimate of a statistic of interest. Agents incur
private costs to reveal their data and the costs can be arbitrarily correlated
with their data. Once revealed, data are verifiable. This paper focuses on
linear unbiased estimators. We design an individually rational and incentive
compatible mechanism that optimizes the worst-case mean-squared error of the
estimation, where the worst-case is over the unknown correlation between costs
and data, subject to a budget constraint in expectation. We characterize the
form of the optimal mechanism in closed-form. We further extend our results to
acquiring data for estimating a parameter in regression analysis, where private
costs can correlate with the values of the dependent variable but not with the
values of the independent variables
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