9 research outputs found
Fast Non-Parametric Bayesian Inference on Infinite Trees
Given i.i.d. data from an unknown distribution, we consider the problem of
predicting future items. An adaptive way to estimate the probability density is
to recursively subdivide the domain to an appropriate data-dependent
granularity. A Bayesian would assign a data-independent prior probability to
"subdivide", which leads to a prior over infinite(ly many) trees. We derive an
exact, fast, and simple inference algorithm for such a prior, for the data
evidence, the predictive distribution, the effective model dimension, and other
quantities.Comment: 8 twocolumn pages, 3 figure
Fast non-parametric Bayesian inference on infinite trees
Given i.i.d. data from an unknown distribution,
we consider the problem of predicting future items.
An adaptive way to estimate the probability density
is to recursively subdivide the domain to an appropriate
data-dependent granularity. A Bayesian would assign a
data-independent prior probability to "subdivide", which leads
to a prior over infinite(ly many) trees. We derive an exact, fast,
and simple inference algorithm for such a prior, for the data
evidence, the predictive distribution, the effective model
dimension, and other quantities
Bayesian Regression of Piecewise Constant Functions
We derive an exact and efficient Bayesian regression algorithm for piecewise
constant functions of unknown segment number, boundary location, and levels. It
works for any noise and segment level prior, e.g. Cauchy which can handle
outliers. We derive simple but good estimates for the in-segment variance. We
also propose a Bayesian regression curve as a better way of smoothing data
without blurring boundaries. The Bayesian approach also allows straightforward
determination of the evidence, break probabilities and error estimates, useful
for model selection and significance and robustness studies. We discuss the
performance on synthetic and real-world examples. Many possible extensions will
be discussed.Comment: 27 pages, 18 figures, 1 table, 3 algorithm
Exact Non-Parametric Bayesian Inference on Infinite Trees
Given i.i.d. data from an unknown distribution, we consider the problem of
predicting future items. An adaptive way to estimate the probability density is
to recursively subdivide the domain to an appropriate data-dependent
granularity. A Bayesian would assign a data-independent prior probability to
"subdivide", which leads to a prior over infinite(ly many) trees. We derive an
exact, fast, and simple inference algorithm for such a prior, for the data
evidence, the predictive distribution, the effective model dimension, moments,
and other quantities. We prove asymptotic convergence and consistency results,
and illustrate the behavior of our model on some prototypical functions.Comment: 32 LaTeX pages, 9 figures, 5 theorems, 1 algorith
Context models on sequences of covers
We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a random walk within the sequence of covers. We demonstrate the approach on problems of conditional density estimation, which, to our knowledge is the first closed-form, non-parametric Bayesian approach to this proble
Fast Non-Parametric Bayesian Inference on Infinite Trees
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A Bayesian would assign a data-independent prior probability to "subdivide", which leads to a prior over infinite(ly many) trees. We derive an exact, fast, and simple inference algorithm for such a prior, for the data evidence, the predictive distribution, the effective model dimension, and other quantities
Fast Non-Parametric Bayesian Inference on Infinite Trees
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate datadependent granularity. A Bayesian would assign a data-independent prior probability to “subdivide”, which leads to a prior over infinite(ly many) trees. We derive an exact, fast, and simple inference algorithm for such a prior, for the data evidence, the predictive distribution, the effective model dimension, and other quantities.