5,222 research outputs found
Symbolic Exact Inference for Discrete Probabilistic Programs
The computational burden of probabilistic inference remains a hurdle for
applying probabilistic programming languages to practical problems of interest.
In this work, we provide a semantic and algorithmic foundation for efficient
exact inference on discrete-valued finite-domain imperative probabilistic
programs. We leverage and generalize efficient inference procedures for
Bayesian networks, which exploit the structure of the network to decompose the
inference task, thereby avoiding full path enumeration. To do this, we first
compile probabilistic programs to a symbolic representation. Then we adapt
techniques from the probabilistic logic programming and artificial intelligence
communities in order to perform inference on the symbolic representation. We
formalize our approach, prove it sound, and experimentally validate it against
existing exact and approximate inference techniques. We show that our inference
approach is competitive with inference procedures specialized for Bayesian
networks, thereby expanding the class of probabilistic programs that can be
practically analyzed
On the Relationship between Sum-Product Networks and Bayesian Networks
In this paper, we establish some theoretical connections between Sum-Product
Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be
converted into a BN in linear time and space in terms of the network size. The
key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent
the local conditional probability distributions at each node in the resulting
BN by exploiting context-specific independence (CSI). The generated BN has a
simple directed bipartite graphical structure. We show that by applying the
Variable Elimination algorithm (VE) to the generated BN with ADD
representations, we can recover the original SPN where the SPN can be viewed as
a history record or caching of the VE inference process. To help state the
proof clearly, we introduce the notion of {\em normal} SPN and present a
theoretical analysis of the consistency and decomposability properties. We
conclude the paper with some discussion of the implications of the proof and
establish a connection between the depth of an SPN and a lower bound of the
tree-width of its corresponding BN.Comment: Full version of the same paper to appear at ICML-201
Tractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference
Exchangeability is a central notion in statistics and probability theory. The
assumption that an infinite sequence of data points is exchangeable is at the
core of Bayesian statistics. However, finite exchangeability as a statistical
property that renders probabilistic inference tractable is less
well-understood. We develop a theory of finite exchangeability and its relation
to tractable probabilistic inference. The theory is complementary to that of
independence and conditional independence. We show that tractable inference in
probabilistic models with high treewidth and millions of variables can be
understood using the notion of finite (partial) exchangeability. We also show
that existing lifted inference algorithms implicitly utilize a combination of
conditional independence and partial exchangeability.Comment: In Proceedings of the 28th AAAI Conference on Artificial Intelligenc
Numeric Input Relations for Relational Learning with Applications to Community Structure Analysis
Most work in the area of statistical relational learning (SRL) is focussed on
discrete data, even though a few approaches for hybrid SRL models have been
proposed that combine numerical and discrete variables. In this paper we
distinguish numerical random variables for which a probability distribution is
defined by the model from numerical input variables that are only used for
conditioning the distribution of discrete response variables. We show how
numerical input relations can very easily be used in the Relational Bayesian
Network framework, and that existing inference and learning methods need only
minor adjustments to be applied in this generalized setting. The resulting
framework provides natural relational extensions of classical probabilistic
models for categorical data. We demonstrate the usefulness of RBN models with
numeric input relations by several examples.
In particular, we use the augmented RBN framework to define probabilistic
models for multi-relational (social) networks in which the probability of a
link between two nodes depends on numeric latent feature vectors associated
with the nodes. A generic learning procedure can be used to obtain a
maximum-likelihood fit of model parameters and latent feature values for a
variety of models that can be expressed in the high-level RBN representation.
Specifically, we propose a model that allows us to interpret learned latent
feature values as community centrality degrees by which we can identify nodes
that are central for one community, that are hubs between communities, or that
are isolated nodes. In a multi-relational setting, the model also provides a
characterization of how different relations are associated with each community
Neural Probabilistic Logic Programming in Discrete-Continuous Domains
Neural-symbolic AI (NeSy) allows neural networks to exploit symbolic
background knowledge in the form of logic. It has been shown to aid learning in
the limited data regime and to facilitate inference on out-of-distribution
data. Probabilistic NeSy focuses on integrating neural networks with both logic
and probability theory, which additionally allows learning under uncertainty. A
major limitation of current probabilistic NeSy systems, such as DeepProbLog, is
their restriction to finite probability distributions, i.e., discrete random
variables. In contrast, deep probabilistic programming (DPP) excels in
modelling and optimising continuous probability distributions. Hence, we
introduce DeepSeaProbLog, a neural probabilistic logic programming language
that incorporates DPP techniques into NeSy. Doing so results in the support of
inference and learning of both discrete and continuous probability
distributions under logical constraints. Our main contributions are 1) the
semantics of DeepSeaProbLog and its corresponding inference algorithm, 2) a
proven asymptotically unbiased learning algorithm, and 3) a series of
experiments that illustrate the versatility of our approach.Comment: 27 pages, 9 figure
AutoBayes: A System for Generating Data Analysis Programs from Statistical Models
Data analysis is an important scientific task which is required whenever information needs to be extracted from raw data. Statistical approaches to data analysis, which use methods from probability theory and numerical analysis, are well-founded but difficult to implement: the development of a statistical data analysis program for any given application is time-consuming and requires substantial knowledge and experience in several areas. In this paper, we describe AutoBayes, a program synthesis system for the generation of data analysis programs from statistical models. A statistical model specifies the properties for each problem variable (i.e., observation or parameter) and its dependencies in the form of a probability distribution. It is a fully declarative problem description, similar in spirit to a set of differential equations. From such a model, AutoBayes generates optimized and fully commented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Code is produced by a schema-guided deductive synthesis process. A schema consists of a code template and applicability constraints which are checked against the model during synthesis using theorem proving technology. AutoBayes augments schema-guided synthesis by symbolic-algebraic computation and can thus derive closed-form solutions for many problems. It is well-suited for tasks like estimating best-fitting model parameters for the given data. Here, we describe AutoBayes's system architecture, in particular the schema-guided synthesis kernel. Its capabilities are illustrated by a number of advanced textbook examples and benchmarks
Logical Abstractions for Noisy Variational Quantum Algorithm Simulation
Due to the unreliability and limited capacity of existing quantum computer
prototypes, quantum circuit simulation continues to be a vital tool for
validating next generation quantum computers and for studying variational
quantum algorithms, which are among the leading candidates for useful quantum
computation. Existing quantum circuit simulators do not address the common
traits of variational algorithms, namely: 1) their ability to work with noisy
qubits and operations, 2) their repeated execution of the same circuits but
with different parameters, and 3) the fact that they sample from circuit final
wavefunctions to drive a classical optimization routine. We present a quantum
circuit simulation toolchain based on logical abstractions targeted for
simulating variational algorithms. Our proposed toolchain encodes quantum
amplitudes and noise probabilities in a probabilistic graphical model, and it
compiles the circuits to logical formulas that support efficient repeated
simulation of and sampling from quantum circuits for different parameters.
Compared to state-of-the-art state vector and density matrix quantum circuit
simulators, our simulation approach offers greater performance when sampling
from noisy circuits with at least eight to 20 qubits and with around 12
operations on each qubit, making the approach ideal for simulating near-term
variational quantum algorithms. And for simulating noise-free shallow quantum
circuits with 32 qubits, our simulation approach offers a reduction
in sampling cost versus quantum circuit simulation techniques based on tensor
network contraction.Comment: ASPLOS '21, April 19-23, 2021, Virtual, US
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