Stability result for a popular algorithm in optimal transport.
problem Stability of the Iterative Proportional Fitting Procedure in time and metric.
method Uniform stability analysis in the 1-Wasserstein metric.
result Quantitative stability result for entropy-regularized Optimal Transport and Schrödinger bridges.
Paper provides exponential convergence guarantees for Iterative Markovian Fitting.
problem Addressing the Schrödinger Bridge problem in computational optimal transport and generative modeling.
method Develops non-asymptotic exponential convergence guarantees for Iterative Markovian Fitting.
result First non-asymptotic exponential convergence guarantees for IMF under mild structural assumptions.
New insights into using IPF for inferring dynamic networks from marginals.
problem Inferring dynamic networks from time-aggregated adjacency matrices and time-varying marginals.
method Identifying a generative network model and establishing its maximum likelihood estimates via IPF, with convergence guarantees for sparse data.
result IPF provides principled estimation of dynamic networks from marginals under certain conditions, with structure-dependent error bounds and guaranteed convergence for sparse data.
A new algorithm reconstructs population dynamics from coarse samples.
problem Reconstructing population dynamics from unlabeled samples at coarse time intervals.
method Deep Momentum Multi-Marginal Schrödinger Bridge (DMSB) framework.
result Significantly outperforms baselines in synthetic and real-world datasets.
A framework estimates categorical distributions under constraints, ensuring generality and uniqueness.
problem Estimating categorical distributions summarizing sample data under marginal constraints.
method Theoretical framework + Iterative Proportional Fitting (IPF) to estimate the distribution.
result A unique categorical distribution of Maximum Entropy under marginal constraints exists and is estimated.
This paper refines the Gaussian Sinkhorn algorithm for general multivariate models.
problem Finite-dimensional solutions for general Gaussian multivariate models.
method Recursive formulation of the Sinkhorn algorithm for Gaussian models, including closed form expressions of entropic transport maps and Schrödinger bridges.
result Refined convergence analysis of Gaussian Sinkhorn algorithms.
Ancestral graph models, introduced by Richardson and Spirtes (2002), generalize both Markov random fields and Bayesian networks to a class of graphs with a global Markov property that is closed under conditioning and marginalization. By design, ancestral graphs encode precisely the conditional independence structures t…
The Sinkhorn-Knopp derivatives converge with linear rate.
problem Optimal transport problem with entropic regularization.
method Iterative proportional fitting procedure.
result Derivatives converge with linear rate.
Consider a reference Markov process with initial distribution π0 and transition kernels {Mt}t∈[1:T], for some T∈N. Assume that you are given distribution πT, which is not equal to the marginal distribution of the reference process at time T. In this scenario, Schrödinger addressed t…
EGMU optimizes portfolios using KL divergence, ensuring positive solutions.
problem Constructing multi-factor target-exposure portfolios efficiently and accurately.
method Convex optimization framework minimizing KL divergence, with explicit solvers.
result Established feasibility and uniqueness of strictly positive solutions under convex-hull conditions.
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define …
New method solves tree-structured Schrödinger Bridge problems.
problem Computing Schrödinger Bridge between tree-structured distributions.
method Iterative Markovian Fitting (IMF) procedure for tree-structured costs.
result Extends IMF to tree-structured Schrödinger Bridge problems.
A new method for fast, non-iterative graphical model estimation.
problem Scalability issues in iterative proportional fitting for high-dimensional data.
method Non-iterative approach for positive definite graphical model estimation.
result The proposed method outperforms state-of-the-art methods in high-dimensional settings.
New method uses optimal transport for better covariate matching in causal effect estimation.
problem Estimating causal effects in observational studies with high-dimensional covariates.
method Multimarginal unbalanced optimal transport for interpretable matching.
result Method provides interpretable weights and competitive performance with k-nearest neighbors.
Paper creates transparent, safe synthetic data from coarsened margins.
problem Creating synthetic data that maintains original relationships and is safe from disclosure.
method Defining and curating margins, applying SDC, coarsening counts, and using IPF algorithm.
result Synthetic data derived from safe, coarsened margins maintains original relationships.
A new method for modeling insurance claim frequencies using random proportions.
problem Inaccurate fitting of classical distributions to insurance claim frequency data.
method Modeling claim frequencies using random proportions of insurance contracts and applying goodness-of-fit tests.
result A new statistical approach for better modeling insurance claim frequencies.
CMCD sampler connects transport and variational inference for efficient sampling.
problem Efficient sampling and generative modeling in Bayesian computation.
method Developed a principled framework using divergences on path space, CMCD sampler with adaptive dynamics.
result CMCD sampler outperforms competing approaches across various experiments.
Kernel Multigrid accelerates Back-fitting for additive Gaussian Processes.
problem Slow convergence of Back-fitting in training additive Gaussian Processes.
method Kernel Packets (KP) and Sparse Gaussian Process Regression (GPR) to enhance Back-fitting.
result Kernel Multigrid reduces the required iterations to O(logn). We present the use of the fitted Q iteration in algorithmic trading. We show that the fitted Q iteration helps alleviate the dimension problem that the basic Q-learning algorithm faces in application to trading. Furthermore, we introduce a procedure including model fitting and data simulation to enrich training data as…
This paper revisits the classic iterative proportional scaling (IPS) from a modern optimization perspective. In contrast to the criticisms made in the literature, we show that based on a coordinate descent characterization, IPS can be slightly modified to deliver coefficient estimates, and from a majorization-minimizat…
The study prevents model collapse in overparameterized linear regression by mixing real and synthetic labels.
problem Preventing model collapse in overparameterized linear regression.
method Iterative mixing of real and synthetic labels, deriving generalization error formulae.
result Optimal mixing ratio converges to the reciprocal of the golden ratio for isotropic features.
The Sinkhorn flow converges to a Wasserstein mirror gradient flow from the Sinkhorn algorithm.
problem Optimizing joint distributions using the Sinkhorn algorithm.
method Wasserstein mirror gradient flow derived from the Sinkhorn algorithm.
result The Sinkhorn flow converges to a Wasserstein mirror gradient flow.
New methods for time-to-event prediction are proposed by extending the Cox proportional hazards model with neural networks. Building on methodology from nested case-control studies, we propose a loss function that scales well to large data sets, and enables fitting of both proportional and non-proportional extensions o…
DSB approximates SB problem for faster generative modeling.
problem Fast generation from complex data distributions.
method Entropy-regularized optimal transport on path spaces.
result DSB yields faster convergence to data distribution.
Develops a method to estimate average hazard under non-proportional hazards without relying on proportional hazards assumption.
problem Estimation of treatment effects when hazards are non-proportional, leading to unstable hazard ratios.
method Semiparametric, doubly robust framework for covariate-adjusted average hazard estimation.
result Valid sqrt{n} inference with small bias and near-nominal confidence-interval coverage across proportional and non-proportional hazards settings.
FVI method calculates bicausal OT with neural networks, outperforming other methods.
problem Computing bicausal optimal transport with adapted coupling structures.
method FVI method using multilayer neural networks to approximate value functions.
result FVI method outperforms linear programming and Sinkhorn methods in scalability.
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Alg…
Learning with label proportions (LLP), which is a learning task that only provides unlabeled data in bags and each bag's label proportion, has widespread successful applications in practice. However, most of the existing LLP methods don't consider the knowledge transfer for uncertain data. This paper presents a transfe…
Variable selection in high dimensional space has challenged many contemporary statistical problems from many frontiers of scientific disciplines. Recent technology advance has made it possible to collect a huge amount of covariate information such as microarray, proteomic and SNP data via bioimaging technology while ob…
Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being a special case of limited dependent data, the models also apply to variables tha…
The κ-generalised distribution fits daily stock returns well.
problem Stock returns are often heavy-tailed, not normally distributed.
method Used the κ-generalised distribution with a Monte-Carlo goodness of fit test. result The κ-generalised distribution fits historic daily stock returns well for a significant proportion of analyzed stocks. Semi-parametric survival analysis methods like the Cox Proportional Hazards (CPH) regression (Cox, 1972) are a popular approach for survival analysis. These methods involve fitting of the log-proportional hazard as a function of the covariates and are convenient as they do not require estimation of the baseline hazard …
Study examines how insurance affects households prone to proportional losses, especially those near poverty.
problem Impact of insurance on households susceptible to proportional losses, focusing on poverty traps.
method Modelled proportional capital losses with insurance, derived closed formulae and non-local differential equations.
result New formulae and methods to calculate trapping probability, constraints on parameters to prevent certainty of trapping.
Study shows how varying levels of supervision and orthonormality constraints affect generalization errors in subspace fitting.
problem Effects of varying levels of supervision and orthonormality constraints on generalization errors in subspace fitting.
method Flexible family of problems connecting unsupervised and supervised subspace fitting tasks, explored over a supervision-orthonormality plane.
result Generalization errors of subspace fitting problems follow double descent trends as they become more supervised and less orthonormally constrained.
We propose a method for efficient training of Q-functions for continuous-state Markov Decision Processes (MDPs) such that the traces of the resulting policies satisfy a given Linear Temporal Logic (LTL) property. LTL, a modal logic, can express a wide range of time-dependent logical properties (including "safety") that…
Population synthesis is concerned with the generation of synthetic yet realistic representations of populations. It is a fundamental problem in the modeling of transport where the synthetic populations of micro-agents represent a key input to most agent-based models. In this paper, a new methodological framework for ho…
Aioli unifies language model data mixing methods and improves performance.
problem Optimizing the mixture of training data groups for language models.
method Unified optimization framework for dynamically adjusting mixture proportions.
result Aioli outperforms existing methods by up to 12.012 test perplexity points.
We propose a sampling scheme suitable for reducing a data set prior to selecting a hypothesis with minimum empirical risk. The sampling only considers a subset of the ultimate (unknown) hypothesis set, but can nonetheless guarantee that the final excess risk will compare favorably with utilizing the entire original dat…
Study ridge ensembles in proportional feature-to-sample size regime, proving risk equivalence and GCV consistency.
problem Characterizing and optimizing ridge ensembles in proportional feature-to-sample size regimes.
method Proportional asymptotics analysis, GCV for tuning, proving risk equivalence.
result Risk of optimal full ridgeless ensemble matches optimal ridge predictor's risk.
Flexible DNN for survival data, avoiding proportional hazards assumption.
problem Survival analysis with complex interactions and non-proportional hazards.
method Partially linear DNN model with a flexible nonparametric component.
result FLEXI-Haz achieves optimal convergence rates and asymptotic efficiency.
New methods improve stability of Sinkhorn algorithm in machine learning.
problem Stability of Sinkhorn semigroups in high-dimensional settings.
method Semigroup analysis based on contraction coefficients and Lyapunov-type operator-theoretic techniques.
result Unified and simplified arguments in Sinkhorn algorithm stability.
Improved KSD test for better detection of differences in distributions.
problem Low power of KSD test when distributions have same modes but different mixing proportions.
method Perturb the observed sample using Markov transition kernels to improve KSD test power.
result Perturbed KSD test can lead to substantially higher power than the original KSD test.
Optimal unimodal fitting for linear loss functions in a sequential, efficient manner.
problem Optimal unimodal transformation of univariate model scores under linear loss functions.
method Proposes a sequential approach to estimate the optimal rectangular fit for observed samples with each new sample.
result Sequential approach achieves optimal efficiency with logarithmic time complexity per iteration.
Exact LAD line fitting via PALB with linear scaling and speed.
problem Robust line fitting for data with outliers.
method Piecewise Affine Lower-Bounding (PALB) method using supporting lines and subdivision scheme.
result Empirical log-linear scaling and significantly faster than LP and IRLS methods.
We give a simple and effective two stage algorithm for approximating a point cloud S⊂Rm by a simplicial complex K. The first stage is an iterative fitting procedure that generalizes k-means clustering, while the second stage involves deleting redundant simplices. A form of dimension reduct…
Iterative algorithms, like gradient descent, are common tools for solving a variety of problems, such as model fitting. For this reason, there is interest in creating differentially private versions of them. However, their conversion to differentially private algorithms is often naive. For instance, a fixed number of i…
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are very fast and simple. In this paper we analyze ILTS in the setting of mixed linear …
Developed an efficient iterative algorithm for SVI model.
problem SVI model's optimizer's strong dependence on input starting point.
method Fixed-point and least-square optimizer.
result Convergence results for fixed-point iterative algorithm in certain situations.