34 accepted papers
Probabilistic forecasting of multivariate time series is challenging due to non-stationarity, inter-variable dependencies, and distribution shifts. While recent diffusion and flow matching models have shown promise, they often ignore informative priors such as conditional means and covariances. In t…
We investigate optimal transport (OT) for measures on graph metric spaces with different total masses. To mitigate the limitations of traditional $L^p$ geometry, Orlicz-Wasserstein (OW) and generalized Sobolev transport (GST) employ \emph{Orlicz geometric structure}, leveraging convex functions to c…
Amortized simulation-based inference (SBI) methods train neural networks on simulated data to perform Bayesian inference. While this strategy avoids the need for tractable likelihoods, it often requires a large number of simulations and has been challenging to scale to time series data. Scientific s…
Flow matching (FM) has gained significant attention as a simulation-free generative model. Unlike diffusion models, which are based on stochastic differential equations, FM employs a simpler approach by solving an ordinary differential equation with an initial condition from a normal distribution, t…
In this paper, we propose a flow-based method for learning all-to-all transfer maps among conditional distributions that approximates pairwise optimal transport. The proposed method addresses the challenge of handling the case of continuous conditions, which often involve a large set of conditions w…
We investigate the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and is obtained by constraining a critic function within a unit ball defined by the Sobolev norm. In particular, it has been…
We study the optimal transport (OT) problem for measures supported on a graph metric space. Recently, Le et al. (2022) leverage the graph structure and propose a variant of OT, namely Sobolev transport (ST), which yields a closed-form expression for a fast computation. However, ST is essentially cou…
Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory and corresponding assumptions on the form of data. We pro…
Kernel conditional mean embeddings (CMEs) offer a powerful framework for representing conditional distributions, but they often face scalability and expressiveness challenges. In this work, we propose a new method that effectively combines the strengths of deep learning with CMEs in order to address…
We study optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying tree structure over supports of input measures. In practice,…
Variational autoencoders (VAEs) are one of the deep generative models that have experienced enormous success over the past decades. However, in practice, they suffer from a problem called posterior collapse, which occurs when the posterior distribution coincides, or collapses, with the prior taking…
Optimal transport (OT) is a popular and powerful tool for comparing probability measures. However, OT suffers a few drawbacks: (i) input measures required to have the same mass, (ii) a high computational complexity, and (iii) indefiniteness which limits its applications on kernel-dependent algorithm…
Supervised transfer learning has received considerable attention due to its potential to boost the predictive power of machine learning in scenarios where data are scarce. Generally, a given set of source models and a dataset from a target domain are used to adapt the pre-trained models to a target…
As an important problem in causal inference, we discuss the identification and estimation of treatment effects (TEs) under limited overlap; that is, when subjects with certain features belong to a single treatment group. We use a latent variable to model a prognostic score which is widely used in bi…
Deep Neural Networks inherit spurious correlations embedded in training data and hence may fail to predict desired labels on unseen domains (or environments), which have different distributions from the domain to provide training data. Invariance Learning (IL) has been developed recently to overcome…
In this study, we present \textit{meta-sequential prediction} (MSP), an unsupervised framework to learn the symmetry from the time sequence of length at least three. Our method leverages the stationary property~(e.g. constant velocity, constant acceleration) of the time sequence to learn the underl…
We propose a novel framework that unifies and extends existing methods of transfer learning (TL) for regression. To bridge a pretrained source model to the model on a target task, we introduce a density-ratio reweighting function, which is estimated through the Bayesian framework with a specific pri…
The inaccessibility of controlled randomized trials due to inherent constraints in many fields of science has been a fundamental issue in causal inference. In this paper, we focus on distinguishing the cause from effect in the bivariate setting under limited observational data. Based on recent devel…
We address the problem of distinguishing cause from effect in bivariate setting. Based on recent developments in nonlinear independent component analysis (ICA), we train general nonlinear causal models that are implemented by neural networks and allow non-additive noise. Further, we build an ensembl…
Matching two different sets of items, called heterogeneous set-to-set matching problem, has recently received attention as a promising problem. The difficulties are to extract features to match a correct pair of different sets and also preserve two types of exchangeability required for set-to-set ma…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams are very sensitive to perturbations in the input space. In t…
Generative adversarial networks, or GANs, commonly display unstable behavior during training. In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive conditions that guarantee eventual stationarity of the generato…
We elucidate a theoretical reason that deep neural networks (DNNs) perform better than other models in some cases from the viewpoint of their statistical properties for non-smooth functions. While DNNs have empirically shown higher performance than other standard methods, understanding its mechanism…
Measuring divergence between two distributions is essential in machine learning and statistics and has various applications including binary classification, change point detection, and two-sample test. Furthermore, in the era of big data, designing divergence measure that is interpretable and can ha…
We theoretically study the landscape of the training error for neural networks in overparameterized cases. We consider three basic methods for embedding a network into a wider one with more hidden units, and discuss whether a minimum point of the narrower network gives a minimum or saddle point of…
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants of OT in the recent literature, one of the most notable bei…
We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why the approach works…
Finding a set of statistically significant features from complex data (e.g., nonlinear and/or multi-dimensional output data) is important for scientific discovery and has a number of practical applications including biomarker discovery. In this paper, we propose a kernel-based post-selection inferen…
While a typical supervised learning framework assumes that the inputs and the outputs are measured at the same levels of granularity, many applications, including global mapping of disease, only have access to outputs at a much coarser level than that of the inputs. Aggregation of outputs makes gene…
We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the false negative rate. These features are constructed via Stein'…
Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation proceudre can be vulnerable to corrupted data points, which often pushes the estimated ratio toward infinity. In this paper, we present a…
Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super-$¥sqrt{n}$ convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where i…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy topological properties. This paper proposes a kernel method on persis…
We learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable option. We introduce a novel concept called the \emphpartition…