Related papers: A Rigorous Link Between Self-Organizing Maps and G…
State-space models (SSM) are central to describe time-varying complex systems in countless signal processing applications such as remote sensing, networks, biomedicine, and finance to name a few. Inference and prediction in SSMs are…
The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…
We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace…
Determining the number of clusters in a dataset is a fundamental issue in data clustering. Many methods have been proposed to solve the problem of selecting the number of clusters, considering it to be a problem with regard to model…
Lifted inference reduces the complexity of inference in relational probabilistic models by identifying groups of constants (or atoms) which behave symmetric to each other. A number of techniques have been proposed in the literature for…
The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. First, we discuss…
Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
This work analyzes the convergence of a class of smoothing-based gradient descent methods when applied to optimization problems. In particular, Gaussian smoothing is employed to define a nonlocal gradient that reduces high-frequency noise,…
This work describes the implementation and application of a correlation determination method based on Self Organizing Maps and Bayesian Inference (SOMBI). SOMBI aims to automatically identify relations between different observed parameters…
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an iterative algorithm for identifying a linear subspace of R^n from data consisting of partial observations of random vectors from that subspace. This paper examines local…
Weak gravitational lensing maps compactly encode the evolution of cosmic large-scale structure and are a key tool for cosmological analyses. Performing inference directly at the map level allows flexible choices of statistics and can…
Kohonen Maps, aka. Self-organizing maps (SOMs) are neural networks that visualize a high-dimensional feature space on a low-dimensional map. While SOMs are an excellent tool for data examination and exploration, they inherently cause a loss…
Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of…
The leading correction to the smoothed connected energy density-density correlation function is obtained for the large energy difference, within the context of the Gaussian Random Matrix Theory. In order to achieve this result, the…
Future 3D semantic occupancy forecasting and motion planning are central to autonomous driving, as they require models to reason about how surrounding scenes evolve and how the ego vehicle should act. Existing occupancy world models…
We present an approach for efficiently training Gaussian Mixture Model (GMM) by Stochastic Gradient Descent (SGD) with non-stationary, high-dimensional streaming data. Our training scheme does not require data-driven parameter…
Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…
How do score-based generative models (SBMs) learn the data distribution supported on a low-dimensional manifold? We investigate the score model of a trained SBM through its linear approximations and subspaces spanned by local feature…
Computer-aided molecular design (CAMD) studies quantitative structure-property relationships and discovers desired molecules using optimization algorithms. With the emergence of machine learning models, CAMD score functions may be replaced…