10,981 research outputs found
Bayesian Updating and Uncertainty Quantification using Sequential Tempered MCMC with the Rank-One Modified Metropolis Algorithm
Bayesian methods are critical for quantifying the behaviors of systems. They
capture our uncertainty about a system's behavior using probability
distributions and update this understanding as new information becomes
available. Probabilistic predictions that incorporate this uncertainty can then
be made to evaluate system performance and make decisions. While Bayesian
methods are very useful, they are often computationally intensive. This
necessitates the development of more efficient algorithms. Here, we discuss a
group of population Markov Chain Monte Carlo (MCMC) methods for Bayesian
updating and system reliability assessment that we call Sequential Tempered
MCMC (ST-MCMC) algorithms. These algorithms combine 1) a notion of tempering to
gradually transform a population of samples from the prior to the posterior
through a series of intermediate distributions, 2) importance resampling, and
3) MCMC. They are a form of Sequential Monte Carlo and include algorithms like
Transitional Markov Chain Monte Carlo and Subset Simulation. We also introduce
a new sampling algorithm called the Rank-One Modified Metropolis Algorithm
(ROMMA), which builds upon the Modified Metropolis Algorithm used within Subset
Simulation to improve performance in high dimensions. Finally, we formulate a
single algorithm to solve combined Bayesian updating and reliability assessment
problems to make posterior assessments of system reliability. The algorithms
are then illustrated by performing prior and posterior reliability assessment
of a water distribution system with unknown leaks and demands
Representing Meaning with a Combination of Logical and Distributional Models
NLP tasks differ in the semantic information they require, and at this time
no single se- mantic representation fulfills all requirements. Logic-based
representations characterize sentence structure, but do not capture the graded
aspect of meaning. Distributional models give graded similarity ratings for
words and phrases, but do not capture sentence structure in the same detail as
logic-based approaches. So it has been argued that the two are complementary.
We adopt a hybrid approach that combines logic-based and distributional
semantics through probabilistic logic inference in Markov Logic Networks
(MLNs). In this paper, we focus on the three components of a practical system
integrating logical and distributional models: 1) Parsing and task
representation is the logic-based part where input problems are represented in
probabilistic logic. This is quite different from representing them in standard
first-order logic. 2) For knowledge base construction we form weighted
inference rules. We integrate and compare distributional information with other
sources, notably WordNet and an existing paraphrase collection. In particular,
we use our system to evaluate distributional lexical entailment approaches. We
use a variant of Robinson resolution to determine the necessary inference
rules. More sources can easily be added by mapping them to logical rules; our
system learns a resource-specific weight that corrects for scaling differences
between resources. 3) In discussing probabilistic inference, we show how to
solve the inference problems efficiently. To evaluate our approach, we use the
task of textual entailment (RTE), which can utilize the strengths of both
logic-based and distributional representations. In particular we focus on the
SICK dataset, where we achieve state-of-the-art results.Comment: Special issue of Computational Linguistics on Formal Distributional
Semantics, 201
Venture: a higher-order probabilistic programming platform with programmable inference
We describe Venture, an interactive virtual machine for probabilistic
programming that aims to be sufficiently expressive, extensible, and efficient
for general-purpose use. Like Church, probabilistic models and inference
problems in Venture are specified via a Turing-complete, higher-order
probabilistic language descended from Lisp. Unlike Church, Venture also
provides a compositional language for custom inference strategies built out of
scalable exact and approximate techniques. We also describe four key aspects of
Venture's implementation that build on ideas from probabilistic graphical
models. First, we describe the stochastic procedure interface (SPI) that
specifies and encapsulates primitive random variables. The SPI supports custom
control flow, higher-order probabilistic procedures, partially exchangeable
sequences and ``likelihood-free'' stochastic simulators. It also supports
external models that do inference over latent variables hidden from Venture.
Second, we describe probabilistic execution traces (PETs), which represent
execution histories of Venture programs. PETs capture conditional dependencies,
existential dependencies and exchangeable coupling. Third, we describe
partitions of execution histories called scaffolds that factor global inference
problems into coherent sub-problems. Finally, we describe a family of
stochastic regeneration algorithms for efficiently modifying PET fragments
contained within scaffolds. Stochastic regeneration linear runtime scaling in
cases where many previous approaches scaled quadratically. We show how to use
stochastic regeneration and the SPI to implement general-purpose inference
strategies such as Metropolis-Hastings, Gibbs sampling, and blocked proposals
based on particle Markov chain Monte Carlo and mean-field variational inference
techniques.Comment: 78 page
Contextual Symmetries in Probabilistic Graphical Models
An important approach for efficient inference in probabilistic graphical
models exploits symmetries among objects in the domain. Symmetric variables
(states) are collapsed into meta-variables (meta-states) and inference
algorithms are run over the lifted graphical model instead of the flat one. Our
paper extends existing definitions of symmetry by introducing the novel notion
of contextual symmetry. Two states that are not globally symmetric, can be
contextually symmetric under some specific assignment to a subset of variables,
referred to as the context variables. Contextual symmetry subsumes previous
symmetry definitions and can rep resent a large class of symmetries not
representable earlier. We show how to compute contextual symmetries by reducing
it to the problem of graph isomorphism. We extend previous work on exploiting
symmetries in the MCMC framework to the case of contextual symmetries. Our
experiments on several domains of interest demonstrate that exploiting
contextual symmetries can result in significant computational gains.Comment: 9 Pages, 4 figure
Mapping Generative Models onto a Network of Digital Spiking Neurons
Stochastic neural networks such as Restricted Boltzmann Machines (RBMs) have
been successfully used in applications ranging from speech recognition to image
classification. Inference and learning in these algorithms use a Markov Chain
Monte Carlo procedure called Gibbs sampling, where a logistic function forms
the kernel of this sampler. On the other side of the spectrum, neuromorphic
systems have shown great promise for low-power and parallelized cognitive
computing, but lack well-suited applications and automation procedures. In this
work, we propose a systematic method for bridging the RBM algorithm and digital
neuromorphic systems, with a generative pattern completion task as proof of
concept. For this, we first propose a method of producing the Gibbs sampler
using bio-inspired digital noisy integrate-and-fire neurons. Next, we describe
the process of mapping generative RBMs trained offline onto the IBM TrueNorth
neurosynaptic processor -- a low-power digital neuromorphic VLSI substrate.
Mapping these algorithms onto neuromorphic hardware presents unique challenges
in network connectivity and weight and bias quantization, which, in turn,
require architectural and design strategies for the physical realization.
Generative performance metrics are analyzed to validate the neuromorphic
requirements and to best select the neuron parameters for the model. Lastly, we
describe a design automation procedure which achieves optimal resource usage,
accounting for the novel hardware adaptations. This work represents the first
implementation of generative RBM inference on a neuromorphic VLSI substrate.Comment: A similar version of this manuscript has been submitted to IEEE
TBioCAS for revision in October 201
Monte Carlo Inference via Greedy Importance Sampling
We present a new method for conducting Monte Carlo inference in graphical
models which combines explicit search with generalized importance sampling. The
idea is to reduce the variance of importance sampling by searching for
significant points in the target distribution. We prove that it is possible to
introduce search and still maintain unbiasedness. We then demonstrate our
procedure on a few simple inference tasks and show that it can improve the
inference quality of standard MCMC methods, including Gibbs sampling,
Metropolis sampling, and Hybrid Monte Carlo. This paper extends previous work
which showed how greedy importance sampling could be correctly realized in the
one-dimensional case.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in
Artificial Intelligence (UAI2000
Asymptotically Independent Markov Sampling: a new MCMC scheme for Bayesian Inference
In Bayesian statistics, many problems can be expressed as the evaluation of
the expectation of a quantity of interest with respect to the posterior
distribution. Standard Monte Carlo method is often not applicable because the
encountered posterior distributions cannot be sampled directly. In this case,
the most popular strategies are the importance sampling method, Markov chain
Monte Carlo, and annealing. In this paper, we introduce a new scheme for
Bayesian inference, called Asymptotically Independent Markov Sampling (AIMS),
which is based on the above methods. We derive important ergodic properties of
AIMS. In particular, it is shown that, under certain conditions, the AIMS
algorithm produces a uniformly ergodic Markov chain. The choice of the free
parameters of the algorithm is discussed and recommendations are provided for
this choice, both theoretically and heuristically based. The efficiency of AIMS
is demonstrated with three numerical examples, which include both multi-modal
and higher-dimensional target posterior distributions.Comment: 38 pages, 11 figure
Plant-wide fault and disturbance screening using combined transfer entropy and eigenvector centrality analysis
Finding the source of a disturbance or fault in complex systems such as
industrial chemical processing plants can be a difficult task and consume a
significant number of engineering hours. In many cases, a systematic
elimination procedure is considered to be the only feasible approach but can
cause undesired process upsets. Practitioners desire robust alternative
approaches.
This paper presents an unsupervised, data-driven method for ranking process
elements according to the magnitude and novelty of their influence. Partial
bivariate transfer entropy estimation is used to infer a weighted directed
graph of process elements. Eigenvector centrality is applied to rank network
nodes according to their overall effect. As the ranking of process elements
rely on emerging properties that depend on the aggregate of many connections,
the results are robust to errors in the estimation of individual edge
properties and the inclusion of indirect connections that do not represent the
true causal structure of the process.
A monitoring chart of continuously calculated process element importance
scores over multiple overlapping time regions can assist with incipient fault
detection. Ranking results combined with visual inspection of information
transfer networks is also useful for root cause analysis of known faults and
disturbances. A software implementation of the proposed method is available.Comment: 21 pages, 9 figure
Feature Engineering for Knowledge Base Construction
Knowledge base construction (KBC) is the process of populating a knowledge
base, i.e., a relational database together with inference rules, with
information extracted from documents and structured sources. KBC blurs the
distinction between two traditional database problems, information extraction
and information integration. For the last several years, our group has been
building knowledge bases with scientific collaborators. Using our approach, we
have built knowledge bases that have comparable and sometimes better quality
than those constructed by human volunteers. In contrast to these knowledge
bases, which took experts a decade or more human years to construct, many of
our projects are constructed by a single graduate student.
Our approach to KBC is based on joint probabilistic inference and learning,
but we do not see inference as either a panacea or a magic bullet: inference is
a tool that allows us to be systematic in how we construct, debug, and improve
the quality of such systems. In addition, inference allows us to construct
these systems in a more loosely coupled way than traditional approaches. To
support this idea, we have built the DeepDive system, which has the design goal
of letting the user "think about features---not algorithms." We think of
DeepDive as declarative in that one specifies what they want but not how to get
it. We describe our approach with a focus on feature engineering, which we
argue is an understudied problem relative to its importance to end-to-end
quality
On the likelihood of multiple bit upsets in logic circuits
Soft errors have a significant impact on the circuit reliability at nanoscale
technologies. At the architectural level, soft errors are commonly modeled by a
probabilistic bit-flip model. In developing such abstract fault models, an
important issue to consider is the likelihood of multiple bit errors caused by
particle strikes. This likelihood has been studied to a great extent in
memories, but has not been understood to the same extent in logic circuits. In
this paper, we attempt to quantify the likelihood that a single transient event
can cause multiple bit errors in logic circuits consisting of combinational
gates and flip-flops. In particular, we calculate the conditional probability
of multiple bit-flips given that a single bit flips as a result of the
transient. To calculate this conditional probability, we use a Monte Carlo
technique in which samples are generated using detailed post-layout circuit
simulations. Our experiments on the ISCAS'85 benchmarks and a few other
circuits indicate that, this conditional probability is quite significant and
can be as high as 0.31. Thus we conclude that multiple bit-flips must
necessarily be considered in order to obtain a realistic architectural fault
model for soft errors.Comment: 6 page
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