523 research outputs found
Learning Logistic Circuits
This paper proposes a new classification model called logistic circuits. On
MNIST and Fashion datasets, our learning algorithm outperforms neural networks
that have an order of magnitude more parameters. Yet, logistic circuits have a
distinct origin in symbolic AI, forming a discriminative counterpart to
probabilistic-logical circuits such as ACs, SPNs, and PSDDs. We show that
parameter learning for logistic circuits is convex optimization, and that a
simple local search algorithm can induce strong model structures from data.Comment: Published in the Proceedings of the Thirty-Third AAAI Conference on
Artificial Intelligence (AAAI19
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
Scaling up Probabilistic Inference in Linear and Non-Linear Hybrid Domains by Leveraging Knowledge Compilation.
Weighted model integration (WMI) extends weighted model counting (WMC) in
providing a computational abstraction for probabilistic inference in mixed
discrete-continuous domains. WMC has emerged as an assembly language for
state-of-the-art reasoning in Bayesian networks, factor graphs, probabilistic
programs and probabilistic databases. In this regard, WMI shows immense promise
to be much more widely applicable, especially as many real-world applications
involve attribute and feature spaces that are continuous and mixed.
Nonetheless, state-of-the-art tools for WMI are limited and less mature than
their propositional counterparts. In this work, we propose a new implementation
regime that leverages propositional knowledge compilation for scaling up
inference. In particular, we use sentential decision diagrams, a tractable
representation of Boolean functions, as the underlying model counting and model
enumeration scheme. Our regime performs competitively to state-of-the-art WMI
systems but is also shown to handle a specific class of non-linear constraints
over non-linear potentials.Comment: In proceedings of ICAART, 2020. A version also appears in AAAI
Workshop: Statistical Relational Artificial Intelligence (StarAI), 202
ADDMC: Weighted Model Counting with Algebraic Decision Diagrams
We present an algorithm to compute exact literal-weighted model counts of
Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic
programming and uses Algebraic Decision Diagrams as the primary data structure.
We implement this technique in ADDMC, a new model counter. We empirically
evaluate various heuristics that can be used with ADDMC. We then compare ADDMC
to state-of-the-art exact weighted model counters (Cachet, c2d, d4, and
miniC2D) on 1914 standard model counting benchmarks and show that ADDMC
significantly improves the virtual best solver.Comment: Presented at AAAI 202
Logical Interpretations of Autoencoders
The unification of low-level perception and high-level reasoning is a
long-standing problem in artificial intelligence, which has the potential to
not only bring the areas of logic and learning closer together but also
demonstrate how abstract concepts might emerge from sensory data. Precisely
because deep learning methods dominate perception-based learning, including
vision, speech, and linguistic grammar, there is fast-growing literature on how
to integrate symbolic reasoning and deep learning. Broadly, efforts seem to
fall into three camps: those focused on defining a logic whose formulas capture
deep learning, ones that integrate symbolic constraints in deep learning, and
others that allow neural computations and symbolic reasoning to co-exist
separately, to enjoy the strengths of both worlds. In this paper, we identify
another dimension to this inquiry: what do the hidden layers really capture,
and how can we reason about that logically? In particular, we consider
autoencoders that are widely used for dimensionality reduction and inject a
symbolic generative framework onto the feature layer. This allows us, among
other things, to generate example images for a class to get a sense of what was
learned. Moreover, the modular structure of the proposed model makes it
possible to learn relations over multiple images at a time, as well as handle
noisy labels. Our empirical evaluations show the promise of this inquiry
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