Self Supervised Correlation-based Permutations for Multi-View Clustering

Fusing information from different modalities can enhance data analysis tasks, including clustering. However, existing multi-view clustering (MVC) solutions are limited to specific domains or rely on a suboptimal and computationally demanding two-stage procedure of representation and clustering. We propose an end-to-end deep learning-based MVC framework for general data (image, tabular, etc.). Our approach involves learning meaningful fused data representations with a novel permutation-based canonical correlation objective. Concurrently, we learn cluster assignments by identifying consistent pseudo-labels across multiple views. We demonstrate the effectiveness of our model using ten MVC benchmark datasets. Theoretically, we show that our model approximates the supervised linear discrimination analysis (LDA) representation. Additionally, we provide an error bound induced by false-pseudo label annotations.

Contextual Feature Selection with Conditional Stochastic Gates

We study the problem of contextual feature selection, where the goal is to learn a predictive function while identifying subsets of informative features conditioned on specific contexts. Towards this goal, we generalize the recently proposed stochastic gates (STG) Yamada et al. [2020] by modeling the probabilistic gates as conditional Bernoulli variables whose parameters are predicted based on the contextual variables. Our new scheme, termed conditional-STG (c-STG), comprises two networks: a hypernetwork that establishes the mapping between contextual variables and probabilistic feature selection parameters and a prediction network that maps the selected feature to the response variable. Training the two networks simultaneously ensures the comprehensive incorporation of context and feature selection within a unified model. We provide a theoretical analysis to examine several properties of the proposed framework. Importantly, our model leads to improved flexibility and adaptability of feature selection and, therefore, can better capture the nuances and variations in the data. We apply c-STG to simulated and real-world datasets, including healthcare, housing, and neuroscience, and demonstrate that it effectively selects contextually meaningful features, thereby enhancing predictive performance and interpretability.

Efficient Verification-Based Face Identification

We study the problem of performing face verification with an efficient neural model $f$. The efficiency of $f$ stems from simplifying the face verification problem from an embedding nearest neighbor search into a binary problem; each user has its own neural network $f$. To allow information sharing between different individuals in the training set, we do not train $f$ directly but instead generate the model weights using a hypernetwork $h$. This leads to the generation of a compact personalized model for face identification that can be deployed on edge devices. Key to the method's success is a novel way of generating hard negatives and carefully scheduling the training objectives. Our model leads to a substantially small $f$ requiring only 23k parameters and 5M floating point operations (FLOPS). We use six face verification datasets to demonstrate that our method is on par or better than state-of-the-art models, with a significantly reduced number of parameters and computational burden. Furthermore, we perform an extensive ablation study to demonstrate the importance of each element in our method.

Gappy local conformal auto-encoders for heterogeneous data fusion: in praise of rigidity

Fusing measurements from multiple, heterogeneous, partial sources, observing a common object or process, poses challenges due to the increasing availability of numbers and types of sensors. In this work we propose, implement and validate an end-to-end computational pipeline in the form of a multiple-auto-encoder neural network architecture for this task. The inputs to the pipeline are several sets of partial observations, and the result is a globally consistent latent space, harmonizing (rigidifying, fusing) all measurements. The key enabler is the availability of multiple slightly perturbed measurements of each instance:, local measurement, "bursts", that allows us to estimate the local distortion induced by each instrument. We demonstrate the approach in a sequence of examples, starting with simple two-dimensional data sets and proceeding to a Wi-Fi localization problem and to the solution of a "dynamical puzzle" arising in spatio-temporal observations of the solutions of Partial Differential Equations.

TabADM: Unsupervised Tabular Anomaly Detection with Diffusion Models

Tables are an abundant form of data with use cases across all scientific fields. Real-world datasets often contain anomalous samples that can negatively affect downstream analysis. In this work, we only assume access to contaminated data and present a diffusion-based probabilistic model effective for unsupervised anomaly detection. Our model is trained to learn the density of normal samples by utilizing a unique rejection scheme to attenuate the influence of anomalies on the density estimation. At inference, we identify anomalies as samples in low-density regions. We use real data to demonstrate that our method improves detection capabilities over baselines. Furthermore, our method is relatively stable to the dimension of the data and does not require extensive hyperparameter tuning.

Interpretable Deep Clustering

Clustering is a fundamental learning task widely used as a first step in data analysis. For example, biologists often use cluster assignments to analyze genome sequences, medical records, or images. Since downstream analysis is typically performed at the cluster level, practitioners seek reliable and interpretable clustering models. We propose a new deep-learning framework that predicts interpretable cluster assignments at the instance and cluster levels. First, we present a self-supervised procedure to identify a subset of informative features from each data point. Then, we design a model that predicts cluster assignments and a gate matrix that leads to cluster-level feature selection. We show that the proposed method can reliably predict cluster assignments using synthetic and real data. Furthermore, we verify that our model leads to interpretable results at a sample and cluster level.

Anomaly Detection with Variance Stabilized Density Estimation

Density estimation based anomaly detection schemes typically model anomalies as examples that reside in low-density regions. We propose a modified density estimation problem and demonstrate its effectiveness for anomaly detection. Specifically, we assume the density function of normal samples is uniform in some compact domain. This assumption implies the density function is more stable (with lower variance) around normal samples than anomalies. We first corroborate this assumption empirically using a wide range of real-world data. Then, we design a variance stabilized density estimation problem for maximizing the likelihood of the observed samples while minimizing the variance of the density around normal samples. We introduce an ensemble of autoregressive models to learn the variance stabilized distribution. Finally, we perform an extensive benchmark with 52 datasets demonstrating that our method leads to state-of-the-art results while alleviating the need for data-specific hyperparameter tuning.

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.

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.

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 $S\alpha S$ L\'evy 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 $S\alpha S$ 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 L\'evy-driven stochastic differential equation (SDE), where one-dimensional L\'evy 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.