Related papers: Hierarchical Distribution Matching: a Versatile To…
There have been many attempts to leverage multiple diffusion models for collaborative generation, extending beyond the original domain. A prominent approach involves synchronizing multiple diffusion trajectories by mixing the estimated…
Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
We propose a new approach for solving planning problems with a hierarchical structure, fusing reinforcement learning and MPC planning. Our formulation tightly and elegantly couples the two planning paradigms. It leverages reinforcement…
The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a…
We study the typical properties of polynomial Support Vector Machines within a Statistical Mechanics approach that allows us to analyze the effect of different normalizations of the features. If the normalization is adecuately chosen, there…
Flow matching has emerged as a compelling generative modeling approach that is widely used across domains. To generate data via a flow matching model, an ordinary differential equation (ODE) is numerically solved via forward integration of…
A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…
A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the Latent Class Analysis model, which captures…
This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The…
Score matching is a vital tool for learning the distribution of data with applications across many areas including diffusion processes, energy based modelling, and graphical model estimation. Despite all these applications, little work…
Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one…
Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular…
Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…
The Hierarchical Mixture of Experts (HME) is a well-known tree-based model for regression and classification, based on soft probabilistic splits. In its original formulation it was trained by maximum likelihood, and is therefore prone to…
This paper presents an extension and an elaboration of the theory of differential similarity, which was originally proposed in arXiv:1401.2411 [cs.LG]. The goal is to develop an algorithm for clustering and coding that combines a geometric…
Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy.…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This object is well-studied in the linear case, when the…
We propose a framework to model the distribution of sequential data coming from a set of entities connected in a graph with a known topology. The method is based on a mixture of shared hidden Markov models (HMMs), which are jointly trained…