arXiv subjects

Ofir Lindenbaum

Publications and source records attributed to Ofir Lindenbaum.

At least 55 records · Page 3Linked to original sources

arXiv2023

Neuronal Cell Type Classification using Deep Learning

The brain is likely the most complex organ, given the variety of functions it controls, the number of cells it comprises, and their corresponding diversity. Studying and identifying neurons, the brain's primary building blocks, is a crucial milestone and essential for understanding brain function in health and disease. Recent developments in machine learning have provided advanced abilities for classifying neurons. However, these methods remain black boxes with no explainability and reasoning. This paper aims to provide a robust and explainable deep-learning framework to classify neurons based on their electrophysiological activity. Our analysis is performed on data provided by the Allen Cell Types database containing a survey of biological features derived from single-cell recordings of mice and humans. First, we classify neuronal cell types of mice data to identify excitatory and inhibitory neurons. Then, neurons are categorized to their broad types in humans using domain adaptation from mice data. Lastly, neurons are classified into sub-types based on transgenic mouse lines using deep neural networks in an explainable fashion. We show state-of-the-art results in a dendrite-type classification of excitatory vs. inhibitory neurons and transgenic mouse lines classification. The model is also inherently interpretable, revealing the correlations between neuronal types and their electrophysiological properties.

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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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arXiv2023

Revisiting the Noise Model of Stochastic Gradient Descent

The stochastic gradient noise (SGN) is a significant factor in the success of stochastic gradient descent (SGD). Following the central limit theorem, SGN was initially modeled as Gaussian, and lately, it has been suggested that stochastic gradient noise is better characterized using $SαS$ Lévy distribution. This claim was allegedly refuted and rebounded to the previously suggested Gaussian noise model. This paper presents solid, detailed empirical evidence that SGN is heavy-tailed and better depicted by the $SαS$ distribution. Furthermore, we argue that different parameters in a deep neural network (DNN) hold distinct SGN characteristics throughout training. To more accurately approximate the dynamics of SGD near a local minimum, we construct a novel framework in $\mathbb{R}^N$, based on Lévy-driven stochastic differential equation (SDE), where one-dimensional Lévy processes model each parameter in the DNN. Next, we show that SGN jump intensity (frequency and amplitude) depends on the learning rate decay mechanism (LRdecay); furthermore, we demonstrate empirically that the LRdecay effect may stem from the reduction of the SGN and not the decrease in the step size. Based on our analysis, we examine the mean escape time, trapping probability, and more properties of DNNs near local minima. Finally, we prove that the training process will likely exit from the basin in the direction of parameters with heavier tail SGN. We will share our code for reproducibility.

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arXiv2022

Support Recovery with Stochastic Gates: Theory and Application for Linear Models

Consider the problem of simultaneous estimation and support recovery of the coefficient vector in a linear data model with additive Gaussian noise. We study the problem of estimating the model coefficients based on a recently proposed non-convex regularizer, namely the stochastic gates (STG) [Yamada et al. 2020]. We suggest a new projection-based algorithm for solving the STG regularized minimization problem, and prove convergence and support recovery guarantees of the STG-estimator for a range of random and non-random design matrix setups. Our new algorithm has been shown to outperform the existing STG algorithm and other classical estimators for support recovery in various real and synthetic data analyses.

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arXiv2022

Imbalanced Classification via Explicit Gradient Learning From Augmented Data

Learning from imbalanced data is one of the most significant challenges in real-world classification tasks. In such cases, neural networks performance is substantially impaired due to preference towards the majority class. Existing approaches attempt to eliminate the bias through data re-sampling or re-weighting the loss in the learning process. Still, these methods tend to overfit the minority samples and perform poorly when the structure of the minority class is highly irregular. Here, we propose a novel deep meta-learning technique to augment a given imbalanced dataset with new minority instances. These additional data are incorporated in the classifier's deep-learning process, and their contributions are learned explicitly. The advantage of the proposed method is demonstrated on synthetic and real-world datasets with various imbalance ratios.

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arXiv2022

SG-VAD: Stochastic Gates Based Speech Activity Detection

We propose a novel voice activity detection (VAD) model in a low-resource environment. Our key idea is to model VAD as a denoising task, and construct a network that is designed to identify nuisance features for a speech classification task. We train the model to simultaneously identify irrelevant features while predicting the type of speech event. Our model contains only 7.8K parameters, outperforms the previously proposed methods on the AVA-Speech evaluation set, and provides comparative results on the HAVIC dataset. We present its architecture, experimental results, and ablation study on the model's components. We publish the code and the models here https://www.github.com/jsvir/vad.

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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

Imbalanced Classification via a Tabular Translation GAN

When presented with a binary classification problem where the data exhibits severe class imbalance, most standard predictive methods may fail to accurately model the minority class. We present a model based on Generative Adversarial Networks which uses additional regularization losses to map majority samples to corresponding synthetic minority samples. This translation mechanism encourages the synthesized samples to be close to the class boundary. Furthermore, we explore a selection criterion to retain the most useful of the synthesized samples. Experimental results using several downstream classifiers on a variety of tabular class-imbalanced datasets show that the proposed method improves average precision when compared to alternative re-weighting and oversampling techniques.

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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

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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arXiv2021

$\ell_0$-based Sparse Canonical Correlation Analysis

Canonical Correlation Analysis (CCA) models are powerful for studying the associations between two sets of variables. The canonically correlated representations, termed \textit{canonical variates} are widely used in unsupervised learning to analyze unlabeled multi-modal registered datasets. Despite their success, CCA models may break (or overfit) if the number of variables in either of the modalities exceeds the number of samples. Moreover, often a significant fraction of the variables measures modality-specific information, and thus removing them is beneficial for identifying the \textit{canonically correlated variates}. Here, we propose $\ell_0$-CCA, a method for learning correlated representations based on sparse subsets of variables from two observed modalities. Sparsity is obtained by multiplying the input variables by stochastic gates, whose parameters are learned together with the CCA weights via an $\ell_0$-regularized correlation loss. We further propose $\ell_0$-Deep CCA for solving the problem of non-linear sparse CCA by modeling the correlated representations using deep nets. We demonstrate the efficacy of the method using several synthetic and real examples. Most notably, by gating nuisance input variables, our approach improves the extracted representations compared to other linear, non-linear and sparse CCA-based models.

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arXiv2021

Kernel-based parameter estimation of dynamical systems with unknown observation functions

A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the underlying system's parameters by measuring its time-evolution only once? The key information for performing this estimation lies in the temporal inter-dependencies between the signal and the model. We propose a kernel-based score to compare these dependencies. Our score generalizes a maximum likelihood estimator for a linear model to a general nonlinear setting in an unknown feature space. We estimate the system's underlying parameters by maximizing the proposed score. We demonstrate the accuracy and efficiency of the method using two chaotic dynamical systems - the double pendulum and the Lorenz '63 model.

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arXiv2021

Refined Least Squares for Support Recovery

We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ \myvec{y} = \myvec{X}\myvecθ^* + \myvecω,$$ and $\myvec{X} \in \mathbb{R}^{N \times D}$ which is a (known) Gaussian matrix and $\myvecω \in \mathbb{R}^N$ is an (unknown) Gaussian noise vector, our goal is to recover the support of the (unknown) sparse vector $\myvecθ^* \in \left\{-1,0,1\right\}^D$. To recover the support of the $\myvecθ^*$ we use an average of multiple least squares solutions, each computed based on a subset of the full set of equations. The support is estimated by identifying the most significant coefficients of the average least squares solution. We demonstrate that in a wide variety of settings our method outperforms state-of-the-art support recovery algorithms.

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arXiv2021

LOCA: LOcal Conformal Autoencoder for standardized data coordinates

We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements.Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized latent variables. By leveraging a repeated measurement sampling strategy, we present a method for learning an embedding in $\mathbb{R}^d$ that is isometric to the latent variables of the manifold. These data coordinates, being invariant under smooth changes of variables, enable matching between different instrumental observations of the same phenomenon. Our embedding is obtained using a LOcal Conformal Autoencoder (LOCA), an algorithm that constructs an embedding to rectify deformations by using a local z-scoring procedure while preserving relevant geometric information. We demonstrate the isometric embedding properties of LOCA on various model settings and observe that it exhibits promising interpolation and extrapolation capabilities. Finally, we apply LOCA to single-site Wi-Fi localization data, and to $3$-dimensional curved surface estimation based on a $2$-dimensional projection.

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arXiv2020

The Spectral Underpinning of word2vec

word2vec due to Mikolov \textit{et al.} (2013) is a word embedding method that is widely used in natural language processing. Despite its great success and frequent use, theoretical justification is still lacking. The main contribution of our paper is to propose a rigorous analysis of the highly nonlinear functional of word2vec. Our results suggest that word2vec may be primarily driven by an underlying spectral method. This insight may open the door to obtaining provable guarantees for word2vec. We support these findings by numerical simulations. One fascinating open question is whether the nonlinear properties of word2vec that are not captured by the spectral method are beneficial and, if so, by what mechanism.

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arXiv2020

Randomly Aggregated Least Squares for Support Recovery

We study the problem of exact support recovery: given an (unknown) vector $θ\in \left\{-1,0,1\right\}^D$, we are given access to the noisy measurement $$ y = Xθ+ ω,$$ where $X \in \mathbb{R}^{N \times D}$ is a (known) Gaussian matrix and the noise $ω\in \mathbb{R}^N$ is an (unknown) Gaussian vector. How small we can choose $N$ and still reliably recover the support of $θ$? We present RAWLS (Randomly Aggregated UnWeighted Least Squares Support Recovery): the main idea is to take random subsets of the $N$ equations, perform a least squares recovery over this reduced bit of information and then average over many random subsets. We show that the proposed procedure can provably recover an approximation of $θ$ and demonstrate its use in support recovery through numerical examples.

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arXiv2020

Differentiable Unsupervised Feature Selection based on a Gated Laplacian

Scientific observations may consist of a large number of variables (features). Identifying a subset of meaningful features is often ignored in unsupervised learning, despite its potential for unraveling clear patterns hidden in the ambient space. In this paper, we present a method for unsupervised feature selection, and we demonstrate its use for the task of clustering. We propose a differentiable loss function that combines the Laplacian score, which favors low-frequency features, with a gating mechanism for feature selection. We improve the Laplacian score, by replacing it with a gated variant computed on a subset of features. This subset is obtained using a continuous approximation of Bernoulli variables whose parameters are trained to gate the full feature space. We mathematically motivate the proposed approach and demonstrate that in the high noise regime, it is crucial to compute the Laplacian on the gated inputs, rather than on the full feature set. Experimental demonstration of the efficacy of the proposed approach and its advantage over current baselines is provided using several real-world examples.

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arXiv2020

Variational Diffusion Autoencoders with Random Walk Sampling

Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to approximate a homeomorphism between the data distribution and the sampling space. This is a construction that strives to define the data manifold. A major obstacle to VAEs and GANs, however, is choosing a suitable prior that matches the data topology. Well-known consequences of poorly picked priors are posterior and mode collapse. To our knowledge, no existing method sidesteps this user choice. Conversely, $\textit{diffusion maps}$ automatically infer the data topology and enjoy a rigorous connection to manifold learning, but do not scale easily or provide the inverse homeomorphism (i.e. decoder/generator). We propose a method that combines these approaches into a generative model that inherits the asymptotic guarantees of $\textit{diffusion maps}$ while preserving the scalability of deep models. We prove approximation theoretic results for the dimension dependence of our proposed method. Finally, we demonstrate the effectiveness of our method with various real and synthetic datasets.

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