6,250 research outputs found
Bayesian Inference of Log Determinants
The log-determinant of a kernel matrix appears in a variety of machine
learning problems, ranging from determinantal point processes and generalized
Markov random fields, through to the training of Gaussian processes. Exact
calculation of this term is often intractable when the size of the kernel
matrix exceeds a few thousand. In the spirit of probabilistic numerics, we
reinterpret the problem of computing the log-determinant as a Bayesian
inference problem. In particular, we combine prior knowledge in the form of
bounds from matrix theory and evidence derived from stochastic trace estimation
to obtain probabilistic estimates for the log-determinant and its associated
uncertainty within a given computational budget. Beyond its novelty and
theoretic appeal, the performance of our proposal is competitive with
state-of-the-art approaches to approximating the log-determinant, while also
quantifying the uncertainty due to budget-constrained evidence.Comment: 12 pages, 3 figure
On the Estimation of Nonrandom Signal Coefficients from Jittered Samples
This paper examines the problem of estimating the parameters of a bandlimited
signal from samples corrupted by random jitter (timing noise) and additive iid
Gaussian noise, where the signal lies in the span of a finite basis. For the
presented classical estimation problem, the Cramer-Rao lower bound (CRB) is
computed, and an Expectation-Maximization (EM) algorithm approximating the
maximum likelihood (ML) estimator is developed. Simulations are performed to
study the convergence properties of the EM algorithm and compare the
performance both against the CRB and a basic linear estimator. These
simulations demonstrate that by post-processing the jittered samples with the
proposed EM algorithm, greater jitter can be tolerated, potentially reducing
on-chip ADC power consumption substantially.Comment: 11 pages, 8 figure
Nonlinear State-Space Models for Microeconometric Panel Data
In applied microeconometric panel data analyses, time-constant random effects and first-order Markov chains are the most prevalent structures to account for intertemporal correlations in limited dependent variable models. An example from health economics shows that the addition of a simple autoregressive error terms leads to a more plausible and parsimonious model which also captures the dynamic features better. The computational problems encountered in the estimation of such models - and a broader class formulated in the framework of nonlinear state space models - hampers their widespread use. This paper discusses the application of different nonlinear filtering approaches developed in the time-series literature to these models and suggests that a straightforward algorithm based on sequential Gaussian quadrature can be expected to perform well in this setting. This conjecture is impressively confirmed by an extensive analysis of the example application
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