arXiv subjects

Liam A. Kruse

Publications and source records attributed to Liam A. Kruse.

6 recordsLinked to original sources

arXiv2026

Simplifying Flow Matching Transformations with Low-Rank Mixture Models

Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density. However, this choice of latent density can impose unnecessary complexity on the learned flow transformation due to the topological mismatch between the latent and data densities, leading to slower training and suboptimal performance. In this work, we propose using mixtures of probabilistic principal component analyzers (MPPCA) as the latent density for normalizing flows. We simplify the learned flow transformation by learning a latent distribution that more closely aligns with the data distribution in terms of KL divergence, thus enabling faster convergence and improved generative performance. Critically, MPPCA models can be fit quickly and cheaply using the expectation-maximization algorithm, making them a practical choice for initializing latent distributions even in high-dimensional generative tasks. We validate our method on both tabular and image datasets, demonstrating consistent gains in training efficiency and generation quality compared to baselines.

cs.LG↗

arXiv2025

Scalable Importance Sampling in High Dimensions with Low-Rank Mixture Proposals

Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal distribution, importance sampling allows for more sample-efficient estimation of rare events or tails of distributions. A common choice of proposal density is a Gaussian mixture model (GMM). However, estimating full-rank GMM covariance matrices in high dimensions is a challenging task due to numerical instabilities. In this work, we propose using mixtures of probabilistic principal component analyzers (MPPCA) as the parametric proposal density for importance sampling methods. MPPCA models are a type of low-rank mixture model that can be fit quickly using expectation-maximization, even in high-dimensional spaces. We validate our method on three simulated systems, demonstrating consistent gains in sample efficiency and quality of failure distribution characterization.

stat.ML↗

arXiv2025

Enhanced Importance Sampling through Latent Space Exploration in Normalizing Flows

Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows for more efficient estimation of rare events or tails of distributions. However, importance sampling can fail when the proposal distribution does not effectively cover the target distribution. In this work, we propose a method for more efficient sampling by updating the proposal distribution in the latent space of a normalizing flow. Normalizing flows learn an invertible mapping from a target distribution to a simpler latent distribution. The latent space can be more easily explored during the search for a proposal distribution, and samples from the proposal distribution are recovered in the space of the target distribution via the invertible mapping. We empirically validate our methodology on simulated robotics applications such as autonomous racing and aircraft ground collision avoidance.

cs.RO↗

arXiv2023

Deep Normalizing Flows for State Estimation

Safe and reliable state estimation techniques are a critical component of next-generation robotic systems. Agents in such systems must be able to reason about the intentions and trajectories of other agents for safe and efficient motion planning. However, classical state estimation techniques such as Gaussian filters often lack the expressive power to represent complex underlying distributions, especially if the system dynamics are highly nonlinear or if the interaction outcomes are multi-modal. In this work, we use normalizing flows to learn an expressive representation of the belief over an agent's true state. Furthermore, we improve upon existing architectures for normalizing flows by using more expressive deep neural network architectures to parameterize the flow. We evaluate our method on two robotic state estimation tasks and show that our approach outperforms both classical and modern deep learning-based state estimation baselines.

cs.RO↗

arXiv2022

Uncertainty-Aware Online Merge Planning with Learned Driver Behavior

Safe and reliable autonomy solutions are a critical component of next-generation intelligent transportation systems. Autonomous vehicles in such systems must reason about complex and dynamic driving scenes in real time and anticipate the behavior of nearby drivers. Human driving behavior is highly nuanced and specific to individual traffic participants. For example, drivers might display cooperative or non-cooperative behaviors in the presence of merging vehicles. These behaviors must be estimated and incorporated in the planning process for safe and efficient driving. In this work, we present a framework for estimating the cooperation level of drivers on a freeway and plan merging maneuvers with the drivers' latent behaviors explicitly modeled. The latent parameter estimation problem is solved using a particle filter to approximate the probability distribution over the cooperation level. A partially observable Markov decision process (POMDP) that includes the latent state estimate is solved online to extract a policy for a merging vehicle. We evaluate our method in a high-fidelity automotive simulator against methods that are agnostic to latent states or rely on $\textit{a priori}$ assumptions about actor behavior.

cs.RO↗

arXiv2021

Dyadic Sex Composition and Task Classification Using fNIRS Hyperscanning Data

Hyperscanning with functional near-infrared spectroscopy (fNIRS) is an emerging neuroimaging application that measures the nuanced neural signatures underlying social interactions. Researchers have assessed the effect of sex and task type (e.g., cooperation versus competition) on inter-brain coherence during human-to-human interactions. However, no work has yet used deep learning-based approaches to extract insights into sex and task-based differences in an fNIRS hyperscanning context. This work proposes a convolutional neural network-based approach to dyadic sex composition and task classification for an extensive hyperscanning dataset with $N = 222$ participants. Inter-brain signal similarity computed using dynamic time warping is used as the input data. The proposed approach achieves a maximum classification accuracy of greater than $80$ percent, thereby providing a new avenue for exploring and understanding complex brain behavior.

eess.IV↗