5 research outputs found
Exponential Family Estimation via Adversarial Dynamics Embedding
We present an efficient algorithm for maximum likelihood estimation (MLE) of exponential family models, with a general parametrization of the energy function that includes neural networks. We exploit the primal-dual view of the MLE with a kinetics augmented model to obtain an estimate associated with an adversarial dual sampler. To represent this sampler, we introduce a novel neural architecture, dynamics embedding, that generalizes Hamiltonian Monte-Carlo (HMC). The proposed approach inherits the flexibility of HMC while enabling tractable entropy estimation for the augmented model. By learning both a dual sampler and the primal model simultaneously, and sharing parameters between them, we obviate the requirement to design a separate sampling procedure once the model has been trained, leading to more effective learning. We show that many existing estimators, such as contrastive divergence, pseudo/composite-likelihood, score matching, minimum Stein discrepancy estimator, non-local contrastive objectives, noise-contrastive estimation, and minimum probability flow, are special cases of the proposed approach, each expressed by a different (fixed) dual sampler. An empirical investigation shows that adapting the sampler during MLE can significantly improve on state-of-the-art estimators
Flow-based sampling for lattice field theories
Critical slowing down and topological freezing severely hinder Monte Carlo
sampling of lattice field theories as the continuum limit is approached.
Recently, significant progress has been made in applying a class of generative
machine learning models, known as "flow-based" samplers, to combat these
issues. These generative samplers also enable promising practical improvements
in Monte Carlo sampling, such as fully parallelized configuration generation.
These proceedings review the progress towards this goal and future prospects of
the method.Comment: 21 pages, 7 figures, Plenary talk at the 40th International Symposium
on Lattice Field Theory (Lattice 2023); references adde
CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations
We propose CaSPR, a method to learn object-centric Canonical Spatiotemporal
Point Cloud Representations of dynamically moving or evolving objects. Our goal
is to enable information aggregation over time and the interrogation of object
state at any spatiotemporal neighborhood in the past, observed or not.
Different from previous work, CaSPR learns representations that support
spacetime continuity, are robust to variable and irregularly spacetime-sampled
point clouds, and generalize to unseen object instances. Our approach divides
the problem into two subtasks. First, we explicitly encode time by mapping an
input point cloud sequence to a spatiotemporally-canonicalized object space. We
then leverage this canonicalization to learn a spatiotemporal latent
representation using neural ordinary differential equations and a generative
model of dynamically evolving shapes using continuous normalizing flows. We
demonstrate the effectiveness of our method on several applications including
shape reconstruction, camera pose estimation, continuous spatiotemporal
sequence reconstruction, and correspondence estimation from irregularly or
intermittently sampled observations.Comment: NeurIPS 202
A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems
Mean field games (MFG) and mean field control (MFC) are critical classes of
multi-agent models for efficient analysis of massive populations of interacting
agents. Their areas of application span topics in economics, finance, game
theory, industrial engineering, crowd motion, and more. In this paper, we
provide a flexible machine learning framework for the numerical solution of
potential MFG and MFC models. State-of-the-art numerical methods for solving
such problems utilize spatial discretization that leads to a
curse-of-dimensionality. We approximately solve high-dimensional problems by
combining Lagrangian and Eulerian viewpoints and leveraging recent advances
from machine learning. More precisely, we work with a Lagrangian formulation of
the problem and enforce the underlying Hamilton-Jacobi-Bellman (HJB) equation
that is derived from the Eulerian formulation. Finally, a tailored neural
network parameterization of the MFG/MFC solution helps us avoid any spatial
discretization. Our numerical results include the approximate solution of
100-dimensional instances of optimal transport and crowd motion problems on a
standard work station and a validation using an Eulerian solver in two
dimensions. These results open the door to much-anticipated applications of MFG
and MFC models that were beyond reach with existing numerical methods.Comment: 21 pages, 13 figures, 2 tabl