Ozgur Sumer - Academia.edu (original) (raw)

Papers by Ozgur Sumer

Motivated by stochastic systems in which observed evidence and conditional dependencies between s... more Motivated by stochastic systems in which observed evidence and conditional dependencies between states of the network change over time, and certain quantities of interest (marginal distributions, likelihood estimates etc.) must be updated, we study the problem of adaptive inference in tree-structured Bayesian networks. We describe an algorithm for adaptive inference that handles a broad range of changes to the network and is able to maintain marginal distributions, MAP estimates, and data likelihoods in all expected logarithmic time. We give an implementation of our algorithm and provide experiments that show that the algorithm can yield up to two orders of magnitude speedups on answering queries and responding to dynamic changes over the sum-product algorithm.

Many algorithms and applications involve repeatedly solving variations of the same inference prob... more Many algorithms and applications involve repeatedly solving variations of the same inference problem, for example to introduce new evidence to the model or to change conditional dependencies. As the model is updated, the goal ofadaptive inference is to take advantage of previously computed quantities to perform inference more rapidly than from scratch. In this paper, we present algorithms for adaptive exact inference on general graphs that can be used to efficiently compute marginals and update MAP configurations under arbitrary changes to the input factor graph and its associated elimination tree. After a linear time preprocessing step, our approach enables updates to the model and the computation of any marginal in time that is logarithmic in the size of the input model. Moreover, in contrast to max-product our approach can also be used to update MAP configurations in time that is roughly proportional to the number of updated entries, rather than the size of t...

2009 IEEE/SP 15th Workshop on Statistical Signal Processing, 2009

Many applications involve repeatedly computing the optimal, maximum a posteriori (MAP) configurat... more Many applications involve repeatedly computing the optimal, maximum a posteriori (MAP) configuration of a graphical model as the model changes, often slowly or incrementally over time, e.g., due to input from a user. Small changes to the model often require updating only a small fraction of the MAP configuration, suggesting the possibility of performing updates faster than recomputing from scratch. In this paper we present an algorithm for efficiently performing such updates under arbitrary changes to the model. Our algorithm is within a logarithmic factor of the optimal and is asymptotically never slower than re-computing from-scratch: if a modification to the model requires m updates to the MAP configuration of n random variables, then our algorithm requires O(m log (n/m)) time; re-computing from scratch requires O(n) time. We evaluate the practical effectiveness of our algorithm by considering two problems in genomic signal processing, CpG region segmentation and protein sidechain packing, where a MAP configuration must be repeatedly updated. Our results show significant speedups over recomputing from scratch.

Many algorithms and applications involve repeatedly solving variations of the same inference prob... more Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive inference is to take advantage of what is preserved in the model and perform inference more rapidly than from scratch. In this paper, we describe techniques for adaptive inference on general graphs that support marginal computation and updates to the conditional probabilities and dependencies in logarithmic time. We give experimental results for an implementation of our algorithm, and demonstrate its potential performance benefit in the study of protein structure.

symposium on discrete algorithms, Jan 23, 2005

Let H be a hypergraph with m edges and maximum degree Δ. Gi... more Let H be a hypergraph with m edges and maximum degree Δ. Given ε ≥ 0, a (1 - ε)-vertex-cover is a collection T of vertices which hits at least (1 - ε)m edges. We denote min |T| by τε. Note that T = To is the (full) covering number of H.In this paper we study the performance ratio of the greedy cover algorithm for this "partial vertex cover" problem and compare it to random choice and to optimal fractional cover. For the first time, we prove a performance ratio bound depending only on ε > 0 for an important class of hypergraphs.Let T* be the optimal fractional covering number (ε = 0). Lovász (1975) showed that To ≤ (1 + In Δ)T*, where Δ is the maximum degree, using the greedy cover algorithm; it follows that the greedy cover algorithm has performance ratio ≤ 1 + In Δ.Kearns (1990) introduced the partial vertex cover problem. He proved that the performance ratio of the greedy cover algorithm for the partial vertex cover problem is ≤ 5+2 In m regardless of ε ≥ 0. Later, Slavík (1997a) improved the bound to 1 + In Δ. Kearns' and Slavík's bounds apply to weighted hypergraphs; in this paper we study the unweighted case only.Our main result is that for ε > 0, the performance ratio of the greedy algorithm is ≤ 1 + In(ΔT*/em). As a corollary, we confirm Babai's conjecture that the greedy cover algorithm has a performance ratio ≤ 1+In(1/ε) for regular and uniform hypergraphs. This special case has significant applications. On the other hand we present examples in which the performance ratio reaches In Δ if either one of the conditions of regularity and uniformity is dropped.We also show that the ratio of the greedy (1 - ε)-cover to T* is ≤ 1/ε for all hypergraphs. Note that this bound again does not depend on the parameters of the hypergraph and is the first such bound.We demonstrate the tightness of our bounds by presenting examples of regular and uniform hypergraphs that have performance ratio ≥ In(1/ε) for partial vertex covering. We obtain similar matching upper and lower bounds for the integrality gap of partial covering.We compare the bounds attained by the greedy cover algorithm with random choice. We establish a counterintuitive gap of In(1/ε) in favor of random choice for a class of regular and uniform hypergraphs.

2009 IEEE/SP 15th Workshop on Statistical Signal Processing, 2009

Many algorithms and applications involve repeatedly solving variations of the same inference prob... more Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive inference is to take advantage of what is preserved in the model and perform inference more rapidly than from scratch. In this paper, we describe techniques for adaptive inference on general graphs that support marginal computation and updates to the conditional probabilities and dependencies in logarithmic time. We give experimental results for an implementation of our algorithm, and demonstrate its potential performance benefit in the study of protein structure.

symposium on discrete algorithms, Jan 23, 2005