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.
The paper examines how to test if two learning algorithms produce similar outcomes.
problem Testing if two learning algorithms produce similar outcomes when trained on different data sets.
method Using Total Variation (TV) distance to measure similarity of posterior distributions.
result TV indistinguishable learning rules are equivalent to existing stability notions and can be statistically amplified.
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.
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 1−o(1), where o(1) is of order 1/loglog(1/TV). Parallel sampling for smooth distributions with fast convergence.
problem Efficiently sampling from distributions with smooth densities.
method Parallelization of Langevin algorithms under log-Sobolev inequalities.
result Samples close to target distribution with low KL divergence or TV distance.
Estimates TV distance between autoregressive models under different access models.
problem Estimating the total variation distance between two autoregressive distributions.
method Three access models: sample access, logit access, and noisy logit access; provides query complexity for each.
result Improved query complexity for estimating TV distance in autoregressive models.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
We analyze the performance of the Tukey median estimator under total variation (TV) distance corruptions. Previous results show that under Huber's additive corruption model, the breakdown point is 1/3 for high-dimensional halfspace-symmetric distributions. We show that under TV corruptions, the breakdown point reduces …
A new distance metric derived from information theory and estimation theory.
problem Developing a robust distance metric for complex signal distributions.
method Information-Estimation Metric (IEM) derived from continuous probability density and denoising errors.
result The IEM is a valid global distance metric that adapts to the geometry of complex distributions.
The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shift algorithm, which is one version of the mean-shift process that successively blurs the dataset. The analysis of the bl…
New blurring diffusion models bridge heat dissipation and denoising.
problem Developing a new generative modeling approach.
method Connecting blurring to Gaussian diffusion with non-isotropic noise.
result Proposed Blurring Diffusion Models offer the best of both Gaussian denoising and inverse heat dissipation.
Flow matching KL divergence bound derived for smooth distributions.
problem Estimating smooth distributions efficiently.
method Deterministic upper bound on KL divergence derived from flow-matching loss.
result Flow matching achieves nearly minimax-optimal efficiency under TV distance.
New tester outperforms existing ones in uniformity testing.
problem Improving uniformity testing accuracy in simulations.
method Introducing a Huber loss-based tester.
result Matches the separation of the collisions tester and has Gaussian-like tails.
Stable GFlowNets prevent loss spikes and mode collapse in training.
problem Unstable training of GFlowNets leading to loss spikes and mode collapse.
method Assessed sensitivity of GFlowNet objectives, derived loss-to-TV bounds, and proposed Stable GFlowNets.
result Stable GFlowNets improve training behavior and distributional fidelity.
Paper studies statistical properties of DP data synthesis algorithms based on Bayesian networks.
problem Ensuring differential privacy in synthetic data generation for high-dimensional data.
method Introduces random noise to low-dimensional marginals of a probabilistic graphical model (BN) to achieve differential privacy.
result Establishes a rigorous accuracy guarantee for BN-based DP synthetic data generators using total variation (TV) distance.
BNCR-GAN improves GANs to generate clean images from degraded inputs.
problem Generating clean images from blurred, noisy, and compressed degraded inputs.
method Multiple-generator model with image, blur-kernel, noise, and quality-factor generators, using masking architectures and adaptive consistency losses.
result BNCR-GAN effectively learns clean image generators from degraded images without degradation parameters.
Robustly clusters mixtures of Gaussians even with outliers.
problem Clustering mixtures of statistically separated Gaussians robustly to outliers.
method Uses certifiable hypercontractivity, bounded variance, and anti-concentration of linear projections.
result First efficient algorithm for robust clustering of statistically separated Gaussians mixtures.
Paper proposes a two-stage ranking for personalized TV recommendations.
problem Improving TV recommendation accuracy and efficiency.
method First, identifies potential candidates using user viewing patterns. Then, ranks them based on user preferences and program textual information.
result The proposed model outperforms in recommendation accuracy and efficiency.
Improved learning of multivariate Gaussians with imperfect advice.
problem Learning multivariate Gaussians with inaccurate advice.
method Developed learning algorithms for multivariate Gaussians using imperfect advice.
result Achieved better sample complexity for learning multivariate Gaussians with imperfect advice.
The paper sets sample complexity bounds for learning high-dimensional simplices in noisy data.
problem Learning high-dimensional simplices from noisy data.
method Sample compression techniques and Fourier-based method for noisy observations.
result Established sample complexity bounds for simplex learning in noisy regimes.
HypeGBMS clusters data in hyperbolic space, overcoming Euclidean limitations.
problem Clustering in hierarchical or tree-like datasets in curved spaces.
method Hyperbolic Gaussian Blurring Mean Shift with Möbius-weighted means.
result HypeGBMS effectively captures latent hierarchies in non-Euclidean data.
We study \emph{TV regularization}, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for ℓp-norm TV. The most important among these is ℓ1-norm TV, for whose prox-operator we present a new geometric analysis which unveils a …
Langevin dynamics fails to produce accurate samples even with small score function errors.
problem Robustness of Langevin dynamics to score function errors.
method Analysis of Langevin dynamics and score function errors.
result Langevin dynamics produces a distribution far from the target distribution in TV distance even with small L2 errors in the score function. Polynomial-time algorithm learns high-dimensional halfspaces without labels.
problem Learning high-dimensional halfspaces with margins in polynomial time.
method Contrastive moments and polynomial-time algorithm.
result Establishes the unique and efficient identifiability of the hidden halfspace.
Conventional out-of-distribution (OOD) detection schemes based on variational autoencoder or Random Network Distillation (RND) have been observed to assign lower uncertainty to the OOD than the target distribution. In this work, we discover that such conventional novelty detection schemes are also vulnerable to the blu…
TVS-FNNs can approximate any continuous function on expanded input spaces.
problem Processing a broader range of inputs like sequences and matrices.
method Proving a universal approximation theorem for TVS-FNNs.
result TVS-FNNs can approximate any continuous function on expanded input spaces.
New algorithm reduces TV-denoising to adaptive online learning.
problem Estimating TV-bounded functions from noisy samples.
method Deep connection to Strongly Adaptive online learning; O(nlogn) time algorithm. result Near minimax optimal rate of O(n1/3Cn2/3) under squared error loss. Debiased Wasserstein barycenters improve on entropy regularization in OT.
problem Entropy regularization in OT introduces bias, leading to blurred barycenters.
method Propose debiased Wasserstein barycenters using Sinkhorn iterations.
result Debiased barycenters preserve fast Sinkhorn-like iterations without entropy smoothing bias.
Unified analysis of MPLE for Ising models with bounded operator norm or infinity norm.
problem Estimating Ising models in Total Variation distance with limited samples.
method Maximum Pseudo-Likelihood Estimator (MPLE) for two general classes of Ising models.
result Unified framework for polynomial-time estimation in TV distance for two general classes of Ising models.
This paper improves non-asymptotic bounds for denoising diffusions, focusing on the Ornstein-Uhlenbeck process.
problem Improving non-asymptotic bounds for denoising diffusions, especially for the Ornstein-Uhlenbeck process.
method Explicit non-asymptotic bounds on forward diffusion error in total variation, considering multi-modal data distributions.
result The Ornstein-Uhlenbeck process cannot be significantly improved in terms of reducing terminal time T for multi-modal data distributions. Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as ℓ1 minimization and nuclear norm minimization are…
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited…
Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, the interpretability of PCA remains limited. However, in neuroimaging, it is essential to uncove…
Two new deterministic offspring selection methods reduce statistical distance in SMC and pMCMC.
problem Improving the performance of resampling in SMC methods.
method Proposes two deterministic offspring selection methods to minimize KL divergence and TV distance.
result Our methods outperform or match state-of-the-art resampling schemes on benchmarks.
Computer Vision and machine learning methods were previously used to reveal screen presence of genders in TV and movies. In this work, using head pose, gender detection, and skin color estimation techniques, we demonstrate that the gender disparity in TV in a South Asian country such as Bangladesh exhibits unique chara…
There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain concentration. Existing methods address this problem by constructing an approximat…
This paper accelerates TV regularization algorithms by unrolling proximal gradient descent.
problem Solving Total Variation (TV) regularized problems with iterative algorithms.
method Unrolling proximal gradient descent solvers to learn their parameters.
result Two approaches to compute derivatives through proximal operators improve performance.
New model for shape graph registration with partial matching constraints.
problem Shape graph registration with topological inconsistencies and partial matching.
method Higher order invariant Sobolev metrics, varifolds, inexact variational formulation, SFISTA algorithm.
result Existence of minimizers for variational problem with TV regularization.
A new robust metric compares distributions more accurately than existing methods.
problem Sensitivity to outliers and sampling discrepancy in Wasserstein distances.
method Introducing k-RPW, a partial p-Wasserstein distance.
result k-RPW converges faster to true distance and is more robust to outliers.
Decision trees and shallow neural networks have different geometric complexities, impacting their interpretability and accuracy.
problem The geometric simplicity of decision boundaries in decision trees conflicts with the approximation capabilities of shallow neural networks.
method Analysis of the Radon total variation (RTV) seminorm to compare geometric complexity of decision regions and neural network approximations.
result Smooth barrier scores can approximate decision regions with finite RTV, but their performance depends on the tube-mass condition near the decision boundary.
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the distances themselves. We use this ordinal information along with the low-dimensionality…
RFM uses tangent vector fields to match data on manifolds, analyzing TV convergence for Euler discretization.
problem Matching data on curved manifolds using flow-based models.
method Developed a nonasymptotic TV convergence analysis for RFM samplers using Euler discretization.
result Explicit bounds on TV convergence separating numerical discretization and learning errors.
RL helps optimize TVS fund composition for volatility control.
problem Optimizing fund composition for target volatility strategy under uncertainty.
method Derive analytical solution for Black-Scholes model, use RL for local volatility model.
result RL agents' performance matches BS strategy in LV model.
New algorithm samples from log-concave distributions with high accuracy in polynomial time.
problem Sampling from log-concave distributions with high accuracy in infinity distance.
method Directly converts continuous samples from K with total-variation bounds to samples with infinity bounds. result Output a point ε-close to π in infinity distance with runtime bounds that depend on polylogarithmic and polynomial factors of 1/ε. This paper presents a learning method for convolutional autoencoders (CAEs) for extracting features from images. CAEs can be obtained by utilizing convolutional neural networks to learn an approximation to the identity function in an unsupervised manner. The loss function based on the pixel loss (PL) that is the mean s…
New invariants derived from a modular category for links and 3-manifolds.
problem Developing new invariants for links and 3-manifolds.
method Extracted invariants from a modular category with two simple objects.
result Invariants for 3-manifolds are related by a specific equation.
Improves diffusion models by controlling total variance and signal-to-noise-ratio.
problem Long sampling time in diffusion models.
method Total-Variance/Signal-to-Noise-Ratio (TV/SNR) disentangled framework.
result Improves generation performance by controlling TV and SNR independently.
Study sample complexity of robust binary hypothesis testing under different contamination models.
problem Analyzing the sample complexity of robust binary hypothesis testing under various contamination models.
method Examined three standard contamination models: ε-additive (Huber), ε-subtractive, and ε-total variation (TV). Provided explicit formulas for least favourable distributions and compared sample complexities across models.
result Sample complexities are highly unstable in the contamination parameter ε and comparable up to constant-factor rescaling of ε across models.