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Yuval Kluger

Publications and source records attributed to Yuval Kluger.

At least 19 recordsLinked to original sources
arXiv2026

Density-Reweighted Entropic Optimal Transport: Decoupling Geometry from Sampling Density

Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets. Entropic Optimal Transport (EOT) offers a computationally tractable framework for this task by encoding cross-dataset affinities in a transport plan. However, when two datasets are sampled from geometrically similar low-dimensional structures with substantially different sampling densities, the EOT plan may match points by relative sampling density rather than geometric proximity, yielding geometrically misleading correspondences. To address this issue, we propose a density-reweighted EOT framework in which the influence of sampling density on the transport plan can be discounted to a desired degree, ranging from standard EOT to alignment driven purely by underlying geometry. Under suitable regularity conditions, we establish convergence of the reweighted EOT plan to a family of population-level plans whose dependence on sampling density is made explicit. Through simulations, we show that our approach recovers geometrically faithful correspondences, improving over related EOT-based frameworks when datasets exhibit substantial sampling density disparity.

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arXiv2025

Understanding and Enhancing Mask-Based Pretraining towards Universal Representations

Mask-based pretraining has become a cornerstone of modern large-scale models across language, vision, and recently biology. Despite its empirical success, its role and limits in learning data representations have been unclear. In this work, we show that the behavior of mask-based pretraining can be directly characterized by test risk in high-dimensional minimum-norm ("ridge-less") linear regression, without relying on further model specifications. Further analysis of linear models uncovers several novel aspects of mask-based pretraining. The theoretical framework and its implications have been validated across diverse neural architectures (including MLPs, CNNs, and Transformers) applied to both vision and language tasks. Guided by our theory, we propose an embarrassingly simple yet overlooked pretraining scheme named Randomly Random Mask AutoEncoding (R$^2$MAE), which enforces capturing multi-scale features from data and is able to outperform optimal fixed mask ratio settings in our linear model framework. We implement R$^2$MAE in vision, language, DNA sequence, and single-cell models, where it consistently outperforms standard and more complicated masking schemes, leading to improvements for state-of-the-art models. Our code is available at: https://github.com/MingzeDong/r2mae

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arXiv2025

Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solver

Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula, which relates the diffusion variate $\mathbf{x}_t$ to the posterior mean $\mathbb{E} [\mathbf{x}_0 | \mathbf{x}_t]$, in order to guide the diffusion trajectory with an estimate of the final denoised sample $\mathbf{x}_0$. However, this does not consider information from the measurement $\mathbf{y}$, which must then be integrated downstream. In this work, we propose to estimate the conditional posterior mean $\mathbb{E} [\mathbf{x}_0 | \mathbf{x}_t, \mathbf{y}]$, which can be formulated as the solution to a lightweight, single-parameter maximum likelihood estimation problem. The resulting prediction can be integrated into any standard sampler, resulting in a fast and memory-efficient inverse solver. Our optimizer is amenable to a noise-aware likelihood-based stopping criteria that is robust to measurement noise in $\mathbf{y}$. We demonstrate comparable or improved performance against a wide selection of contemporary inverse solvers across multiple datasets and tasks.

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arXiv2025

Euclidean Distance Deflation Under High-Dimensional Heteroskedastic Noise

Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a prevalent form of inhomogeneous corruption characterized by variable noise magnitudes across data observations. Such noise inflates the computed distances in a nontrivial way, leading to misrepresentations of the underlying data geometry. In this work, we address the tasks of estimating the noise magnitudes per observation and correcting the pairwise Euclidean distances under heteroskedastic noise. Perhaps surprisingly, we show that in general high-dimensional settings and without assuming prior knowledge on the clean data structure or noise distribution, both tasks can be performed reliably, even when the noise levels vary considerably. Specifically, we develop a principled, hyperparameter-free approach that jointly estimates the noise magnitudes and corrects the distances. We provide theoretical guarantees for our approach, establishing probabilistic bounds on the estimation errors of both noise magnitudes and distances. These bounds, measured in the normalized $\ell_1$ norm, converge to zero at polynomial rates as both feature dimension and dataset size increase. Experiments on synthetic datasets demonstrate that our method accurately estimates distances in challenging regimes, significantly improving the robustness of subsequent distance-based computations. Notably, when applied to single-cell RNA sequencing data, our method yields noise magnitude estimates consistent with an established prototypical model, enabling accurate nearest neighbor identification that is fundamental to many downstream analyses.

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arXiv2025

Likelihood Training of Cascaded Diffusion Models via Hierarchical Volume-preserving Maps

Cascaded models are multi-scale generative models with a marked capacity for producing perceptually impressive samples at high resolutions. In this work, we show that they can also be excellent likelihood models, so long as we overcome a fundamental difficulty with probabilistic multi-scale models: the intractability of the likelihood function. Chiefly, in cascaded models each intermediary scale introduces extraneous variables that cannot be tractably marginalized out for likelihood evaluation. This issue vanishes by modeling the diffusion process on latent spaces induced by a class of transformations we call hierarchical volume-preserving maps, which decompose spatially structured data in a hierarchical fashion without introducing local distortions in the latent space. We demonstrate that two such maps are well-known in the literature for multiscale modeling: Laplacian pyramids and wavelet transforms. Not only do such reparameterizations allow the likelihood function to be directly expressed as a joint likelihood over the scales, we show that the Laplacian pyramid and wavelet transform also produces significant improvements to the state-of-the-art on a selection of benchmarks in likelihood modeling, including density estimation, lossless compression, and out-of-distribution detection. Investigating the theoretical basis of our empirical gains we uncover deep connections to score matching under the Earth Mover's Distance (EMD), which is a well-known surrogate for perceptual similarity. Code can be found at \href{https://github.com/lihenryhfl/pcdm}{this https url}.

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arXiv2024

Dual Diffusion for Unified Image Generation and Understanding

Diffusion models have gained tremendous success in text-to-image generation, yet still lag behind with visual understanding tasks, an area dominated by autoregressive vision-language models. We propose a large-scale and fully end-to-end diffusion model for multi-modal understanding and generation that significantly improves on existing diffusion-based multimodal models, and is the first of its kind to support the full suite of vision-language modeling capabilities. Inspired by the multimodal diffusion transformer (MM-DiT) and recent advances in discrete diffusion language modeling, we leverage a cross-modal maximum likelihood estimation framework that simultaneously trains the conditional likelihoods of both images and text jointly under a single loss function, which is back-propagated through both branches of the diffusion transformer. The resulting model is highly flexible and capable of a wide range of tasks including image generation, captioning, and visual question answering. Our model attained competitive performance compared to recent unified image understanding and generation models, demonstrating the potential of multimodal diffusion modeling as a promising alternative to autoregressive next-token prediction models.

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arXiv2024

The Dyson Equalizer: Adaptive Noise Stabilization for Low-Rank Signal Detection and Recovery

Detecting and recovering a low-rank signal in a noisy data matrix is a fundamental task in data analysis. Typically, this task is addressed by inspecting and manipulating the spectrum of the observed data, e.g., thresholding the singular values of the data matrix at a certain critical level. This approach is well-established in the case of homoskedastic noise, where the noise variance is identical across the entries. However, in numerous applications, the noise can be heteroskedastic, where the noise characteristics may vary considerably across the rows and columns of the data. In this scenario, the spectral behavior of the noise can differ significantly from the homoskedastic case, posing various challenges for signal detection and recovery. To address these challenges, we develop an adaptive normalization procedure that equalizes the average noise variance across the rows and columns of a given data matrix. Our proposed procedure is data-driven and fully automatic, supporting a broad range of noise distributions, variance patterns, and signal structures. Our approach relies on recent results in random matrix theory, which describe the resolvent of the noise via the so-called Dyson equation. By leveraging this relation, we can accurately infer the noise level in each row and each column directly from the resolvent of the data. We establish that in many cases, our normalization enforces the standard spectral behavior of homoskedastic noise -- the Marchenko-Pastur (MP) law, allowing for simple and reliable detection of signal components. Furthermore, we demonstrate that our approach can substantially improve signal recovery in heteroskedastic settings by manipulating the spectrum after normalization. Lastly, we apply our method to single-cell RNA sequencing and spatial transcriptomics data, showcasing accurate fits to the MP law after normalization.

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arXiv2024

Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets

Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental conditions. Such datasets may share underlying structures of interest but exhibit individual distortions, resulting in misaligned embeddings using traditional techniques. In this work, we propose Entropic Optimal Transport (EOT) eigenmaps, a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverages the leading singular vectors of the EOT plan matrix between two datasets to extract their shared underlying structure and align them in a common embedding space. We interpret our approach as an inter-data variant of the classical Laplacian eigenmaps and diffusion maps embeddings, showing that it enjoys many favorable analogous properties. We analyze a generative model in which two observed high-dimensional datasets share latent variables supported on a common low-dimensional manifold, while each dataset is subject to translation, geometric distortion, orthogonal nuisance structure, and noise. In a large-sample, high-dimensional regime, we prove that the EOT plan concentrates around a population kernel on an effective manifold determined by the geometric mean of the distortions, with invariance to translations, orthogonal nuisance structure, and noise. Subsequently, we relate our embedding to eigenfunctions of population-level operators encoding the density and geometry of the shared manifold. Finally, we showcase the performance of our approach for data integration and embedding through simulations and analyses of real-world biological data, demonstrating its advantages over alternative methods in challenging scenarios.

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arXiv2023

Exponential weight averaging as damped harmonic motion

The exponential moving average (EMA) is a commonly used statistic for providing stable estimates of stochastic quantities in deep learning optimization. Recently, EMA has seen considerable use in generative models, where it is computed with respect to the model weights, and significantly improves the stability of the inference model during and after training. While the practice of weight averaging at the end of training is well-studied and known to improve estimates of local optima, the benefits of EMA over the course of training is less understood. In this paper, we derive an explicit connection between EMA and a damped harmonic system between two particles, where one particle (the EMA weights) is drawn to the other (the model weights) via an idealized zero-length spring. We then leverage this physical analogy to analyze the effectiveness of EMA, and propose an improved training algorithm, which we call BELAY. Finally, we demonstrate theoretically and empirically several advantages enjoyed by BELAY over standard EMA.

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arXiv2023

Multi-modal Differentiable Unsupervised Feature Selection

Multi-modal high throughput biological data presents a great scientific opportunity and a significant computational challenge. In multi-modal measurements, every sample is observed simultaneously by two or more sets of sensors. In such settings, many observed variables in both modalities are often nuisance and do not carry information about the phenomenon of interest. Here, we propose a multi-modal unsupervised feature selection framework: identifying informative variables based on coupled high-dimensional measurements. Our method is designed to identify features associated with two types of latent low-dimensional structures: (i) shared structures that govern the observations in both modalities and (ii) differential structures that appear in only one modality. To that end, we propose two Laplacian-based scoring operators. We incorporate the scores with differentiable gates that mask nuisance features and enhance the accuracy of the structure captured by the graph Laplacian. The performance of the new scheme is illustrated using synthetic and real datasets, including an extended biological application to single-cell multi-omics.

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arXiv2022

Autoregressive Generative Modeling with Noise Conditional Maximum Likelihood Estimation

We introduce a simple modification to the standard maximum likelihood estimation (MLE) framework. Rather than maximizing a single unconditional likelihood of the data under the model, we maximize a family of \textit{noise conditional} likelihoods consisting of the data perturbed by a continuum of noise levels. We find that models trained this way are more robust to noise, obtain higher test likelihoods, and generate higher quality images. They can also be sampled from via a novel score-based sampling scheme which combats the classical \textit{covariate shift} problem that occurs during sample generation in autoregressive models. Applying this augmentation to autoregressive image models, we obtain 3.32 bits per dimension on the ImageNet 64x64 dataset, and substantially improve the quality of generated samples in terms of the Frechet Inception distance (FID) -- from 37.50 to 12.09 on the CIFAR-10 dataset.

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arXiv2022

Probabilistic Robust Autoencoders for Outlier Detection

Anomalies (or outliers) are prevalent in real-world empirical observations and potentially mask important underlying structures. Accurate identification of anomalous samples is crucial for the success of downstream data analysis tasks. To automatically identify anomalies, we propose Probabilistic Robust AutoEncoder (PRAE). PRAE aims to simultaneously remove outliers and identify a low-dimensional representation for the inlier samples. We first present the Robust AutoEncoder (RAE) objective as a minimization problem for splitting the data into inliers and outliers. Our objective is designed to exclude outliers while including a subset of samples (inliers) that can be effectively reconstructed using an AutoEncoder (AE). RAE minimizes the autoencoder's reconstruction error while incorporating as many samples as possible. This could be formulated via regularization by subtracting an $\ell_0$ norm counting the number of selected samples from the reconstruction term. Unfortunately, this leads to an intractable combinatorial problem. Therefore, we propose two probabilistic relaxations of RAE, which are differentiable and alleviate the need for a combinatorial search. We prove that the solution to the PRAE problem is equivalent to the solution of RAE. We use synthetic data to show that PRAE can accurately remove outliers in a wide range of contamination levels. Finally, we demonstrate that using PRAE for anomaly detection leads to state-of-the-art results on various benchmark datasets.

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arXiv2022

ManiFeSt: Manifold-based Feature Selection for Small Data Sets

In this paper, we present a new method for few-sample supervised feature selection (FS). Our method first learns the manifold of the feature space of each class using kernels capturing multi-feature associations. Then, based on Riemannian geometry, a composite kernel is computed, extracting the differences between the learned feature associations. Finally, a FS score based on spectral analysis is proposed. Considering multi-feature associations makes our method multivariate by design. This in turn allows for the extraction of the hidden manifold underlying the features and avoids overfitting, facilitating few-sample FS. We showcase the efficacy of our method on illustrative examples and several benchmarks, where our method demonstrates higher accuracy in selecting the informative features compared to competing methods. In addition, we show that our FS leads to improved classification and better generalization when applied to test data.

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arXiv2022

Neural Inverse Transform Sampler

Any explicit functional representation $f$ of a density is hampered by two main obstacles when we wish to use it as a generative model: designing $f$ so that sampling is fast, and estimating $Z = \int f$ so that $Z^{-1}f$ integrates to 1. This becomes increasingly complicated as $f$ itself becomes complicated. In this paper, we show that when modeling one-dimensional conditional densities with a neural network, $Z$ can be exactly and efficiently computed by letting the network represent the cumulative distribution function of a target density, and applying a generalized fundamental theorem of calculus. We also derive a fast algorithm for sampling from the resulting representation by the inverse transform method. By extending these principles to higher dimensions, we introduce the \textbf{Neural Inverse Transform Sampler (NITS)}, a novel deep learning framework for modeling and sampling from general, multidimensional, compactly-supported probability densities. NITS is a highly expressive density estimator that boasts end-to-end differentiability, fast sampling, and exact and cheap likelihood evaluation. We demonstrate the applicability of NITS by applying it to realistic, high-dimensional density estimation tasks: likelihood-based generative modeling on the CIFAR-10 dataset, and density estimation on the UCI suite of benchmark datasets, where NITS produces compelling results rivaling or surpassing the state of the art.

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arXiv2022

Locally Sparse Neural Networks for Tabular Biomedical Data

Tabular datasets with low-sample-size or many variables are prevalent in biomedicine. Practitioners in this domain prefer linear or tree-based models over neural networks since the latter are harder to interpret and tend to overfit when applied to tabular datasets. To address these neural networks' shortcomings, we propose an intrinsically interpretable network for heterogeneous biomedical data. We design a locally sparse neural network where the local sparsity is learned to identify the subset of most relevant features for each sample. This sample-specific sparsity is predicted via a \textit{gating} network, which is trained in tandem with the \textit{prediction} network. By forcing the model to select a subset of the most informative features for each sample, we reduce model overfitting in low-sample-size data and obtain an interpretable model. We demonstrate that our method outperforms state-of-the-art models when applied to synthetic or real-world biomedical datasets using extensive experiments. Furthermore, the proposed framework dramatically outperforms existing schemes when evaluating its interpretability capabilities. Finally, we demonstrate the applicability of our model to two important biomedical tasks: survival analysis and marker gene identification.

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arXiv2021

Spectral Top-Down Recovery of Latent Tree Models

Modeling the distribution of high dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nodes. Many algorithms for tree recovery are computationally intensive, which limits their applicability to trees of moderate size. For large trees, a common approach, termed divide-and-conquer, is to recover the tree structure in two steps. First, recover the structure separately of multiple, possibly random subsets of the terminal nodes. Second, merge the resulting subtrees to form a full tree. Here, we develop Spectral Top-Down Recovery (STDR), a deterministic divide-and-conquer approach to infer large latent tree models. Unlike previous methods, STDR partitions the terminal nodes in a non random way, based on the Fiedler vector of a suitable Laplacian matrix related to the observed nodes. We prove that under certain conditions, this partitioning is consistent with the tree structure. This, in turn, leads to a significantly simpler merging procedure of the small subtrees. We prove that STDR is statistically consistent and bound the number of samples required to accurately recover the tree with high probability. Using simulated data from several common tree models in phylogenetics, we demonstrate that STDR has a significant advantage in terms of runtime, with improved or similar accuracy.

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arXiv2021

Biwhitening Reveals the Rank of a Count Matrix

Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the spectral properties of large noise matrices. However, utilizing such tools is not straightforward when the data matrix consists of count random variables, e.g., Poisson, in which case the noise can be heteroskedastic with an unknown variance in each entry. In this work, we consider a Poisson random matrix with independent entries, and propose a simple procedure termed \textit{biwhitening} for estimating the rank of the underlying signal matrix (i.e., the Poisson parameter matrix) without any prior knowledge. Our approach is based on the key observation that one can scale the rows and columns of the data matrix simultaneously so that the spectrum of the corresponding noise agrees with the standard Marchenko-Pastur (MP) law, justifying the use of the MP upper edge as a threshold for rank selection. Importantly, the required scaling factors can be estimated directly from the observations by solving a matrix scaling problem via the Sinkhorn-Knopp algorithm. Aside from the Poisson, our approach is extended to families of distributions that satisfy a quadratic relation between the mean and the variance, such as the generalized Poisson, binomial, negative binomial, gamma, and many others. This quadratic relation can also account for missing entries in the data. We conduct numerical experiments that corroborate our theoretical findings, and showcase the advantage of our approach for rank estimation in challenging regimes. Furthermore, we demonstrate the favorable performance of our approach on several real datasets of single-cell RNA sequencing (scRNA-seq), High-Throughput Chromosome Conformation Capture (Hi-C), and document topic modeling.

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arXiv2021

Deep Unsupervised Feature Selection by Discarding Nuisance and Correlated Features

Modern datasets often contain large subsets of correlated features and nuisance features, which are not or loosely related to the main underlying structures of the data. Nuisance features can be identified using the Laplacian score criterion, which evaluates the importance of a given feature via its consistency with the Graph Laplacians' leading eigenvectors. We demonstrate that in the presence of large numbers of nuisance features, the Laplacian must be computed on the subset of selected features rather than on the complete feature set. To do this, we propose a fully differentiable approach for unsupervised feature selection, utilizing the Laplacian score criterion to avoid the selection of nuisance features. We employ an autoencoder architecture to cope with correlated features, trained to reconstruct the data from the subset of selected features. Building on the recently proposed concrete layer that allows controlling for the number of selected features via architectural design, simplifying the optimization process. Experimenting on several real-world datasets, we demonstrate that our proposed approach outperforms similar approaches designed to avoid only correlated or nuisance features, but not both. Several state-of-the-art clustering results are reported.

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