509 research outputs found
Query DAGs: A Practical Paradigm for Implementing Belief-Network Inference
We describe a new paradigm for implementing inference in belief networks,
which consists of two steps: (1) compiling a belief network into an arithmetic
expression called a Query DAG (Q-DAG); and (2) answering queries using a simple
evaluation algorithm. Each node of a Q-DAG represents a numeric operation, a
number, or a symbol for evidence. Each leaf node of a Q-DAG represents the
answer to a network query, that is, the probability of some event of interest.
It appears that Q-DAGs can be generated using any of the standard algorithms
for exact inference in belief networks (we show how they can be generated using
clustering and conditioning algorithms). The time and space complexity of a
Q-DAG generation algorithm is no worse than the time complexity of the
inference algorithm on which it is based. The complexity of a Q-DAG evaluation
algorithm is linear in the size of the Q-DAG, and such inference amounts to a
standard evaluation of the arithmetic expression it represents. The intended
value of Q-DAGs is in reducing the software and hardware resources required to
utilize belief networks in on-line, real-world applications. The proposed
framework also facilitates the development of on-line inference on different
software and hardware platforms due to the simplicity of the Q-DAG evaluation
algorithm. Interestingly enough, Q-DAGs were found to serve other purposes:
simple techniques for reducing Q-DAGs tend to subsume relatively complex
optimization techniques for belief-network inference, such as network-pruning
and computation-caching.Comment: See http://www.jair.org/ for any accompanying file
Quasipolynomial simulation of DNNF by a non-determinstic read-once branching program
We prove that dnnfs can be simulated by Non-deterministic Read-Once Branching Programs (nrobps) of quasi-polynomial size. As a result, all the exponential lower bounds for nrobps immediately apply for dnnfs
On the read-once property of branching programs and CNFs of bounded treewidth
for non-deterministic (syntactic) read-once branching programs (nrobps) on functions expressible as cnfs with treewidth at most k of their primal graphs. This lower bound rules out the possibility of fixed-parameter space complexity of nrobps parameterized by k. We use lower bound for nrobps to obtain a quasi-polynomial separation between Free Binary Decision Diagrams and Decision Decomposable Negation Normal Forms, essentially matching the existing upper bound introduced by Beame et al. (Proceedings of the twenty-ninth conference on uncertainty in artificial intelligence, Bellevue, 2013) and thus proving the tightness of the latter
Model-Based Diagnosis using Structured System Descriptions
This paper presents a comprehensive approach for model-based diagnosis which
includes proposals for characterizing and computing preferred diagnoses,
assuming that the system description is augmented with a system structure (a
directed graph explicating the interconnections between system components).
Specifically, we first introduce the notion of a consequence, which is a
syntactically unconstrained propositional sentence that characterizes all
consistency-based diagnoses and show that standard characterizations of
diagnoses, such as minimal conflicts, correspond to syntactic variations on a
consequence. Second, we propose a new syntactic variation on the consequence
known as negation normal form (NNF) and discuss its merits compared to standard
variations. Third, we introduce a basic algorithm for computing consequences in
NNF given a structured system description. We show that if the system structure
does not contain cycles, then there is always a linear-size consequence in NNF
which can be computed in linear time. For arbitrary system structures, we show
a precise connection between the complexity of computing consequences and the
topology of the underlying system structure. Finally, we present an algorithm
that enumerates the preferred diagnoses characterized by a consequence. The
algorithm is shown to take linear time in the size of the consequence if the
preference criterion satisfies some general conditions.Comment: See http://www.jair.org/ for any accompanying file
Machine Learning Methods for Septic Shock Prediction
Sepsis is an organ dysfunction life-threatening disease that is caused by a dysregulated body response to infection. Sepsis is difficult to detect at an early stage, and when not detected early, is difficult to treat and results in high mortality rates. Developing improved methods for identifying patients in high risk of suffering septic shock has been the focus of much research in recent years. Building on this body of literature, this dissertation develops an improved method for septic shock prediction. Using the data from the MMIC-III database, an ensemble classifier is trained to identify high-risk patients. A robust prediction model is built by obtaining a risk score from fitting the Cox Hazard model on multiple input features. The score is added to the list of features and the Random Forest ensemble classifier is trained to produce the model. The Cox Enhanced Random Forest (CERF) proposed method is evaluated by comparing its predictive accuracy to those of extant methods
The Language of Search
This paper is concerned with a class of algorithms that perform exhaustive
search on propositional knowledge bases. We show that each of these algorithms
defines and generates a propositional language. Specifically, we show that the
trace of a search can be interpreted as a combinational circuit, and a search
algorithm then defines a propositional language consisting of circuits that are
generated across all possible executions of the algorithm. In particular, we
show that several versions of exhaustive DPLL search correspond to such
well-known languages as FBDD, OBDD, and a precisely-defined subset of d-DNNF.
By thus mapping search algorithms to propositional languages, we provide a
uniform and practical framework in which successful search techniques can be
harnessed for compilation of knowledge into various languages of interest, and
a new methodology whereby the power and limitations of search algorithms can be
understood by looking up the tractability and succinctness of the corresponding
propositional languages
A Knowledge Compilation Map
We propose a perspective on knowledge compilation which calls for analyzing
different compilation approaches according to two key dimensions: the
succinctness of the target compilation language, and the class of queries and
transformations that the language supports in polytime. We then provide a
knowledge compilation map, which analyzes a large number of existing target
compilation languages according to their succinctness and their polytime
transformations and queries. We argue that such analysis is necessary for
placing new compilation approaches within the context of existing ones. We also
go beyond classical, flat target compilation languages based on CNF and DNF,
and consider a richer, nested class based on directed acyclic graphs (such as
OBDDs), which we show to include a relatively large number of target
compilation languages
Parameterized Compilation Lower Bounds for Restricted CNF-formulas
We show unconditional parameterized lower bounds in the area of knowledge
compilation, more specifically on the size of circuits in decomposable negation
normal form (DNNF) that encode CNF-formulas restricted by several graph width
measures. In particular, we show that
- there are CNF formulas of size and modular incidence treewidth
whose smallest DNNF-encoding has size , and
- there are CNF formulas of size and incidence neighborhood diversity
whose smallest DNNF-encoding has size .
These results complement recent upper bounds for compiling CNF into DNNF and
strengthen---quantitatively and qualitatively---known conditional low\-er
bounds for cliquewidth. Moreover, they show that, unlike for many graph
problems, the parameters considered here behave significantly differently from
treewidth
Cliquewidth and knowledge compilation
In this paper we study the role of cliquewidth in succinct representation of Boolean functions. Our main statement is the following: Let Z be a Boolean circuit having cliquewidth k. Then there is another circuit Z * computing the same function as Z having treewidth at most 18k + 2 and which has at most 4|Z| gates where |Z| is the number of gates of Z. In this sense, cliquewidth is not more ‘powerful’ than treewidth for the purpose of representation of Boolean functions. We believe this is quite a surprising fact because it contrasts the situation with graphs where an upper bound on the treewidth implies an upper bound on the cliquewidth but not vice versa.
We demonstrate the usefulness of the new theorem for knowledge compilation. In particular, we show that a circuit Z of cliquewidth k can be compiled into a Decomposable Negation Normal Form (dnnf) of size O(918k k 2|Z|) and the same runtime. To the best of our knowledge, this is the first result on efficient knowledge compilation parameterized by cliquewidth of a Boolean circuit
Complexity Results and Approximation Strategies for MAP Explanations
MAP is the problem of finding a most probable instantiation of a set of
variables given evidence. MAP has always been perceived to be significantly
harder than the related problems of computing the probability of a variable
instantiation Pr, or the problem of computing the most probable explanation
(MPE). This paper investigates the complexity of MAP in Bayesian networks.
Specifically, we show that MAP is complete for NP^PP and provide further
negative complexity results for algorithms based on variable elimination. We
also show that MAP remains hard even when MPE and Pr become easy. For example,
we show that MAP is NP-complete when the networks are restricted to polytrees,
and even then can not be effectively approximated. Given the difficulty of
computing MAP exactly, and the difficulty of approximating MAP while providing
useful guarantees on the resulting approximation, we investigate best effort
approximations. We introduce a generic MAP approximation framework. We provide
two instantiations of the framework; one for networks which are amenable to
exact inference Pr, and one for networks for which even exact inference is too
hard. This allows MAP approximation on networks that are too complex to even
exactly solve the easier problems, Pr and MPE. Experimental results indicate
that using these approximation algorithms provides much better solutions than
standard techniques, and provide accurate MAP estimates in many cases
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