Related papers: Learning Lie Group Generators from Trajectories

Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…

We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. Such…

Retrieval-Augmented Generation (RAG) enhances LLMs by grounding generation in query-relevant external evidence. Beyond unstructured text corpora, Graph RAG integrates knowledge graphs into the retrieval pipeline, enabling LLMs to access…

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees…

A Generative Adversarial Network (GAN) with generator $G$ trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. Here, we propose a new method of deploying a…

We call a unital locally convex algebra $A$ a continuous inverse algebra if its unit group $A^\times$ is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group $G$ on a…

In many learning applications, data are collected from multiple sources, each providing a \emph{batch} of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one…

Without any assumptions about data generation, multiple causal models may explain our observations equally well. To avoid selecting a single arbitrary model that could result in unsafe decisions if it does not match reality, it is therefore…

Mobility trajectories are essential for understanding urban dynamics and enhancing urban planning, yet access to such data is frequently hindered by privacy concerns. This research introduces a transformative framework for generating…

Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough…

Energy-based models for discrete domains, such as graphs, explicitly capture relative likelihoods, naturally enabling composable probabilistic inference tasks like conditional generation or enforcing constraints at test-time. However,…

Pervasive integration of GPS-enabled devices and data acquisition technologies has led to an exponential increase in GPS trajectory data, fostering advancements in spatial-temporal data mining research. Nonetheless, GPS trajectories contain…

In this work, we propose the Generative Latent Flow (GLF), an algorithm for generative modeling of the data distribution. GLF uses an Auto-encoder (AE) to learn latent representations of the data, and a normalizing flow to map the…

The development of robust generative models for highly varied non-stationary time series data is a complex yet important problem. Traditional models for time series data prediction, such as Long Short-Term Memory (LSTM), are inefficient and…

We consider the offline imitation learning from observations (LfO) where the expert demonstrations are scarce and the available offline suboptimal data are far from the expert behavior. Many existing distribution-matching approaches…

We propose Gradient Inversion Transcript (GIT), a novel generative approach for reconstructing training data from leaked gradients. GIT employs a generative attack model, whose architecture is tailored to align with the structure of the…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…

A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a…

It is difficult to anticipate the myriad challenges that a predictive model will encounter once deployed. Common practice entails a reactive, cyclical approach: model deployment, data mining, and retraining. We instead develop a proactive…

Learning interpretable and human-controllable representations that uncover factors of variation in data remains an ongoing key challenge in representation learning. We investigate learning group-disentangled representations for groups of…