Conceitos essenciais
Learning subtractive mixture models through squaring can lead to more expressive and efficient representations compared to traditional additive mixture models.
Resumo
The content discusses the concept of subtractive mixture models represented by squaring in the context of probabilistic circuits. It explores the theoretical foundations, practical implications, and empirical evidence supporting the increased expressiveness and efficiency of these models. The discussion covers various aspects such as representation, learning, inference, and comparisons with traditional models on both synthetic and real-world data sets.
Abstract:
- Introduces subtractive mixture models via squaring.
- Investigates theoretical expressiveness and practical applications.
- Empirically demonstrates improved distribution estimation tasks.
Introduction:
- Discusses finite mixture models in probabilistic machine learning.
- Highlights the challenge of ensuring valid distributions in non-monotonic mixtures.
- Introduces the concept of squaring linear combinations for subtractive mixtures.
Subtractive Mixtures via Squaring:
- Formalizes representation of shallow NMMs by squaring non-convex combinations.
- Explores tractable marginalization and conditioning in squared NMMs.
- Discusses numerical stability in inference and learning processes.
Squaring Deep Mixture Models:
- Generalizes shallow mixtures to deep tensorized circuits for tractable inference.
- Defines tensorized circuits for modeling possibly negative functions.
- Proposes an algorithm for efficiently squaring tensorized structured-decomposable circuits.
Expressiveness of NPC2s:
- Examines how NPC2s compare to structured monotonic PCs in terms of expressiveness.
- Provides theoretical reductions from other model classes to NPC2s.
- Demonstrates experimentally superior performance of NPC2s on various data sets.
Experiments:
A) Synthetic Continuous Data:
- Evaluates monotonic PCs and NPC2s on 2D density estimation tasks with splines as input layers.
B) Synthetic Discrete Data:
- Estimates probability mass functions on discretized 2D data sets using categoricals or Binomials as input layers for MPCs and NPC2s.
C) Multi-variate Continuous Data:
- Compares log-likelihood performance between monotonic PCs and NPC2s on multivariate data sets using randomized linear tree RG structures.
Distilling Intractable Models:
- Investigates distillation performance of GPT2 onto monotonic PCs vs. NPC2s for text generation tasks.
Estatísticas
"NPC2s can approximate distributions better than monotonic PCs."
"Squared NMM encodes a distribution over variables X."
"Tractable marginalization supported by squared NMMs."
Citações
"Squaring ensures non-negativity but allows tractable renormalization."
"NPC2s can be exponentially more expressive than structured monotonic PCs."