Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a g…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “Total-Variation”
Optimal Pre-Processing to Achieve Fairness and Its Relationship with Total Variation Barycentercs.IT
Optimal pre-processing reduces disparate impact by minimizing total variation distance.
problem Achieving fairness in data outputs based on protected attributes.
method Using pre-processing to enforce fairness, minimizing total variation distance between pre-processed and original data distributions.
result The problem of fairness can be formulated as a linear program, efficiently solvable.
The paper studies curves in Riemannian manifolds using total variation flow.
problem Analyzing the evolution of curves in Riemannian manifolds using total variation.
method Defining and proving the existence of strong solutions to the flow equations, showing variational equality, and proving convergence.
result Strong solutions converge to a constant map in finite time for non-positive sectional curvature.
The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in . This distance plays a fundamental role in machine learning and signal processing: It is a member of the broader class of -divergences, and it is related to …
We consider the problem of estimating a function defined over locations on a -dimensional grid (having all side lengths equal to ). When the function is constrained to have discrete total variation bounded by , we derive the minimax optimal (squared) estimation error rate, parametrized by …
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularize…
SaR-SVM-STV improves hyperspectral image classification with shape-adaptive reconstruction and denoising.
problem Classifying hyperspectral images with limited labeled data.
method Shape-adaptive Reconstruction (SaR) for pixel preprocessing, SVM for probability estimation, and Smoothed Total Variation (STV) for denoising.
result SaR-SVM-STV outperforms SVM-STV with fewer labeled data.
Estimates parameters of interconnected linear systems using total variation penalization.
problem Joint estimation of parameters in interconnected linear dynamical systems.
method Total variation penalized least-squares estimator.
result The MSE goes to zero as the number of systems increases, even with constant trajectory length.
Sharp inequality between TV and Hellinger distances for Gaussian mixtures.
problem Understanding the relationship between total variation and Hellinger distances for Gaussian mixtures.
method Established a general upper bound on Hellinger distance in terms of TV distance raised to a power, demonstrating sharpness with specific examples.
result The Hellinger distance between two Gaussian mixtures is bounded by the TV distance raised to a power , where is of order .
Discriminative Estimation of Total Variation Distance: A Fidelity Auditor for Generative Datastat.ML
Paper proposes a method to estimate total variation distance for synthetic data fidelity.
problem Assessing the fidelity of synthetic data generated by AI.
method Discriminative approach to estimate total variation distance between two distributions.
result Estimation of total variation distance reduces to quantifying Bayes risk in classification.
We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding Lovász extensions and the squared Euclidean norm, leading to algorithms requiring …
Proximal algorithms applied to current deformation into cycles.
problem Deformation of de Rham currents into cycles.
method Proximal algorithms, total variation denoising for differential forms.
result Calibrated cycles constructed in calibrated manifolds.
Example shows learnable distributions not privately learnable.
problem Learnable distributions under non-private conditions not transferable to differential privacy.
method Example of a distribution class learnable up to constant error in total variation distance but not under differential privacy.
result Contradicts conjecture of Ashtiani on learnability under differential privacy.
Graphs with non-negative Ollivier-Ricci curvature cannot be expanders.
problem Understanding the relationship between graph curvature and expansion properties.
method Proving an inequality linking isoperimetric profiles to total variation decay of random walks.
result Graphs with non-negative Ollivier-Ricci curvature cannot be expanders.
We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised images that are piecewise constant on rectangular sets. We prove that, if the t…
The paper shows diffusion models can converge faster to a target distribution with low-dimensional structure.
problem Improving the convergence rate of diffusion models to target distributions.
method Analyzing DDIM and DDPM samplers under low-dimensional structure assumptions.
result The iteration complexities of DDIM and DDPM are no greater than in total variation distance.
A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster ass…
Error estimates found between SGD with momentum and Langevin diffusion.
problem Quantifying the difference between SGD with momentum and Langevin diffusion.
method Established error estimates using 1-Wasserstein and total variation distances.
result Quantitative error estimates between SGD with momentum and underdamped Langevin diffusion.
New method relaxes TV distance for two-sample testing without distributional assumptions.
problem Challenges in certifying equality or providing tight bounds on TV distance for two distributions.
method Examined blurred total variation distance, a relaxation of TV distance.
result Provided theoretical guarantees for upper and lower bounds on blurred TV distance.
We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total…
Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only applicable under special conditions. In this paper, we present a new learning frame…
New bounds on neural network convergence using information theory.
problem Quantifying convergence rates of neural networks to Gaussian distributions.
method Entropic inequalities and Gaussian approximations.
result Improved convergence rates in various distances for neural networks.
Algorithm learns affine transformations robustly from corrupted samples.
problem Learning affine transformations from corrupted samples.
method New geometric certificate and iterative improvement method.
result Total variation distance of between learned and original distributions.
Efficiently estimates binary product distributions with privacy.
problem Estimating means of binary product distributions privately and accurately.
method Polynomial time, pure differential privacy approach.
result Optimal sample complexity with polylogarithmic factors.
Proves sufficiency of countable test plans for BV functions on metric spaces.
problem Recovering BV functions and their measures on arbitrary metric spaces.
method Proves sufficiency of countable test plans on arbitrary metric measure spaces and geodesics on spaces.
result Countable test plans are sufficient for BV functions and their measures on metric spaces.
Robust Bayesian inference improves model performance on discrete data.
problem Misspecification of discrete-valued models leads to poor inference and prediction.
method Total Variation Distance (TVD) for discrepancy, efficient estimator and inference method.
result Our approach significantly improves predictive performance on various data.
In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an…
While it is believed that denoising is not always necessary in many big data applications, we show in this paper that denoising is helpful in urban traffic analysis by applying the method of bounded total variation denoising to the urban road traffic prediction and clustering problem. We propose two easy-to-implement m…
We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to develop mathematical tools needed to study the consistency, as the number of availa…
Reinforcement learning mimics expert behavior.
problem Learning from expert demonstrations in reinforcement learning.
method Reduction to reinforcement learning with a stationary reward.
result Expert reward can be recovered and imitation learning is bounded.
New characterization limits sampling with inexact scores.
problem Limiting sampling with inexact scores for unbiased results.
method Characterized types of inexact score oracle access.
result Weaker error assumptions rule out tractability of unbiased sampling.
Method estimates noise transition matrix from noisy labels without relying on unreliable class-posterior estimation.
problem Estimating noise transition matrix from noisy data.
method Total variation regularization to encourage distinguishable predicted probabilities.
result Consistent estimator of the noise transition matrix under mild assumptions.
Based on a study of the coupling by reflection of diffusion processes, a new monotonicity in time of a time-dependent transportation cost between heat distribution is shown under Bakry-Emery's curvature-dimension condition on a Riemannian manifold. The cost function comes from the total variation between heat distribut…
Paper introduces a new method to model epidemic dynamics with varying parameters.
problem Capturing discontinuous variations in epidemic model parameters.
method Total variation regularization with Iterated Nelder--Mead optimization.
result The method accurately models epidemic dynamics with instant changes.
New schemes improve error estimates for sampling from non-log-concave distributions.
problem Improving sampling from non-log-concave distributions with super-linear drift growth.
method Developed tamed Euler and randomized Euler schemes with error estimates.
result Near-optimal error bounds for sampling and optimization problems.
uHMC achieves fast mixing in high dimensions with gradient evaluations.
problem Quantifying mixing time of uHMC in high dimensions.
method Construction of successful couplings for uHMC.
result uHMC mixes in total variation with logarithmic dependence on dimension.
New method for tensor completion using nonconvex dual total variation.
problem Tensor completion from partial measurements with exponential-family noise.
method Proposed dual-TV (DTV) regularizers for tensor completion under exponential-family noise.
result Theoretical upper bounds on recovery error for tensor completion.
We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the comp…
Data clustering is a fundamental problem with a wide range of applications. Standard methods, eg the -means method, usually require solving a non-convex optimization problem. Recently, total variation based convex relaxation to the -means model has emerged as an attractive alternative for data clustering. However…
Spatially-sparse predictors are good models for brain decoding: they give accurate predictions and their weight maps are interpretable as they focus on a small number of regions. However, the state of the art, based on total variation or graph-net, is computationally costly. Here we introduce sparsity in the local neig…
New framework estimates staged tree models using hierarchical clustering on the probability simplex.
problem Estimating staged tree models with context-specific dependencies.
method Hierarchical clustering on the probability simplex, using simplex-based divergences and linkage methods.
result Total Variation divergence with Ward.D2 linkage produces staged trees with better model fit, structure recovery, and computational efficiency.
Study shows private learning of mixtures of Gaussians is possible with polynomial samples.
problem Estimating mixtures of Gaussians under differential privacy constraints.
method Developed a new framework for privately learning mixtures of Gaussians without structural assumptions.
result Polynomial number of samples (poly(k,d,1/α,1/ε,log(1/δ))) sufficient for estimation up to total variation distance α with (ε, δ)-DP.
The Minimum Description Length (MDL) principle selects the model that has the shortest code for data plus model. We show that for a countable class of models, MDL predictions are close to the true distribution in a strong sense. The result is completely general. No independence, ergodicity, stationarity, identifiabilit…
Estimating the level set of a signal from measurements is a task that arises in a variety of fields, including medical imaging, astronomy, and digital elevation mapping. Motivated by scenarios where accurate and complete measurements of the signal may not available, we examine here a simple procedure for estimating the…
Paper explores robust estimators for kernel exponential families using smoothed total variation distances.
problem Outliers can severely impact classical estimators in statistical inference.
method Proposes smoothed total variation (STV) distance as a class of IPMs for robust estimation of kernel exponential families.
result STV-based estimators are robust against distribution contamination for kernel exponential families.
The study improves PAC-Bayesian bounds for adversarial generative models.
problem Improving generalization bounds for adversarial generative models.
method Extending PAC-Bayesian theory to generative models, developing bounds for Wasserstein and total variation distances.
result New training objectives for Wasserstein and Energy-Based GANs.
This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using …
We study density estimation for classes of shift-invariant distributions over . A multidimensional distribution is "shift-invariant" if, roughly speaking, it is close in total variation distance to a small shift of it in any direction. Shift-invariance relaxes smoothness assumptions commonly used in non-p…