8,239 research outputs found
A Method of Moments for Mixture Models and Hidden Markov Models
Mixture models are a fundamental tool in applied statistics and machine
learning for treating data taken from multiple subpopulations. The current
practice for estimating the parameters of such models relies on local search
heuristics (e.g., the EM algorithm) which are prone to failure, and existing
consistent methods are unfavorable due to their high computational and sample
complexity which typically scale exponentially with the number of mixture
components. This work develops an efficient method of moments approach to
parameter estimation for a broad class of high-dimensional mixture models with
many components, including multi-view mixtures of Gaussians (such as mixtures
of axis-aligned Gaussians) and hidden Markov models. The new method leads to
rigorous unsupervised learning results for mixture models that were not
achieved by previous works; and, because of its simplicity, it offers a viable
alternative to EM for practical deployment
An Extension of Slow Feature Analysis for Nonlinear Blind Source Separation
We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a reliability of more than \%. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources
Automatic Bayesian Density Analysis
Making sense of a dataset in an automatic and unsupervised fashion is a
challenging problem in statistics and AI. Classical approaches for {exploratory
data analysis} are usually not flexible enough to deal with the uncertainty
inherent to real-world data: they are often restricted to fixed latent
interaction models and homogeneous likelihoods; they are sensitive to missing,
corrupt and anomalous data; moreover, their expressiveness generally comes at
the price of intractable inference. As a result, supervision from statisticians
is usually needed to find the right model for the data. However, since domain
experts are not necessarily also experts in statistics, we propose Automatic
Bayesian Density Analysis (ABDA) to make exploratory data analysis accessible
at large. Specifically, ABDA allows for automatic and efficient missing value
estimation, statistical data type and likelihood discovery, anomaly detection
and dependency structure mining, on top of providing accurate density
estimation. Extensive empirical evidence shows that ABDA is a suitable tool for
automatic exploratory analysis of mixed continuous and discrete tabular data.Comment: In proceedings of the Thirty-Third AAAI Conference on Artificial
Intelligence (AAAI-19
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