18 research outputs found
Maximum a Posteriori Estimation by Search in Probabilistic Programs
We introduce an approximate search algorithm for fast maximum a posteriori
probability estimation in probabilistic programs, which we call Bayesian ascent
Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with
varying number of mutually dependent finite, countable, and continuous random
variables. BaMC is an anytime MAP search algorithm applicable to any
combination of random variables and dependencies. We compare BaMC to other MAP
estimation algorithms and show that BaMC is faster and more robust on a range
of probabilistic models.Comment: To appear in proceedings of SOCS1
Approximate MMAP by Marginal Search
We present a heuristic strategy for marginal MAP (MMAP) queries in graphical
models. The algorithm is based on a reduction of the task to a polynomial
number of marginal inference computations. Given an input evidence, the
marginals mass functions of the variables to be explained are computed.
Marginal information gain is used to decide the variables to be explained
first, and their most probable marginal states are consequently moved to the
evidence. The sequential iteration of this procedure leads to a MMAP
explanation and the minimum information gain obtained during the process can be
regarded as a confidence measure for the explanation. Preliminary experiments
show that the proposed confidence measure is properly detecting instances for
which the algorithm is accurate and, for sufficiently high confidence levels,
the algorithm gives the exact solution or an approximation whose Hamming
distance from the exact one is small.Comment: To be presented at the 33rd International Florida Artificial
Intelligence Research Society Conference (Flairs-33
New Results for the MAP Problem in Bayesian Networks
This paper presents new results for the (partial) maximum a posteriori (MAP)
problem in Bayesian networks, which is the problem of querying the most
probable state configuration of some of the network variables given evidence.
First, it is demonstrated that the problem remains hard even in networks with
very simple topology, such as binary polytrees and simple trees (including the
Naive Bayes structure). Such proofs extend previous complexity results for the
problem. Inapproximability results are also derived in the case of trees if the
number of states per variable is not bounded. Although the problem is shown to
be hard and inapproximable even in very simple scenarios, a new exact algorithm
is described that is empirically fast in networks of bounded treewidth and
bounded number of states per variable. The same algorithm is used as basis of a
Fully Polynomial Time Approximation Scheme for MAP under such assumptions.
Approximation schemes were generally thought to be impossible for this problem,
but we show otherwise for classes of networks that are important in practice.
The algorithms are extensively tested using some well-known networks as well as
random generated cases to show their effectiveness.Comment: A couple of typos were fixed, as well as the notation in part of
section 4, which was misleading. Theoretical and empirical results have not
change