arXiv subjects

Vahid Tarokh

Publications and source records attributed to Vahid Tarokh.

At least 73 records · Page 4Linked to original sources

arXiv2023

Inference and Sampling of Point Processes from Diffusion Excursions

Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this framework, we relate the return times of a diffusion in a continuous path space to new arrivals of the point process. This leads to a continuous sample path that is used to describe the underlying mechanism generating the arrival distribution. These models arise in many disciplines, such as financial settings where actions in a market are determined by a hidden continuous price or in neuroscience where a latent stimulus generates spike trains. Based on the developments in Itô's excursion theory, we propose methods for inferring and sampling from the point process derived from the latent diffusion process. We illustrate the approach with numerical examples using both simulated and real data. The proposed methods and framework provide a basis for interpreting point processes through the lens of diffusions.

stat.CO↗

arXiv2023

Neural Network Accelerated Process Design of Polycrystalline Microstructures

Computational experiments are exploited in finding a well-designed processing path to optimize material structures for desired properties. This requires understanding the interplay between the processing-(micro)structure-property linkages using a multi-scale approach that connects the macro-scale (process parameters) to meso (homogenized properties) and micro (crystallographic texture) scales. Due to the nature of the problem's multi-scale modeling setup, possible processing path choices could grow exponentially as the decision tree becomes deeper, and the traditional simulators' speed reaches a critical computational threshold. To lessen the computational burden for predicting microstructural evolution under given loading conditions, we develop a neural network (NN)-based method with physics-infused constraints. The NN aims to learn the evolution of microstructures under each elementary process. Our method is effective and robust in finding optimal processing paths. In this study, our NN-based method is applied to maximize the homogenized stiffness of a Copper microstructure, and it is found to be 686 times faster while achieving 0.053% error in the resulting homogenized stiffness compared to the traditional finite element simulator on a 10-process experiment.

cs.CE↗

arXiv2023

Minimax Concave Penalty Regularized Adaptive System Identification

We develop a recursive least square (RLS) type algorithm with a minimax concave penalty (MCP) for adaptive identification of a sparse tap-weight vector that represents a communication channel. The proposed algorithm recursively yields its estimate of the tap-vector, from noisy streaming observations of a received signal, using expectation-maximization (EM) update. We prove the convergence of our algorithm to a local optimum and provide bounds for the steady state error. Using simulation studies of Rayleigh fading channel, Volterra system and multivariate time series model, we demonstrate that our algorithm outperforms, in the mean-squared error (MSE) sense, the standard RLS and the $\ell_1$-regularized RLS.

eess.SP↗

arXiv2023

Subspace Perturbation Analysis for Data-Driven Radar Target Localization

Recent works exploring data-driven approaches to classical problems in adaptive radar have demonstrated promising results pertaining to the task of radar target localization. Via the use of space-time adaptive processing (STAP) techniques and convolutional neural networks, these data-driven approaches to target localization have helped benchmark the performance of neural networks for matched scenarios. However, the thorough bridging of these topics across mismatched scenarios still remains an open problem. As such, in this work, we augment our data-driven approach to radar target localization by performing a subspace perturbation analysis, which allows us to benchmark the localization accuracy of our proposed deep learning framework across mismatched scenarios. To evaluate this framework, we generate comprehensive datasets by randomly placing targets of variable strengths in mismatched constrained areas via RFView, a high-fidelity, site-specific modeling and simulation tool. For the radar returns from these constrained areas, we generate heatmap tensors in range, azimuth, and elevation using the normalized adaptive matched filter (NAMF) test statistic. We estimate target locations from these heatmap tensors using a convolutional neural network, and demonstrate that the predictive performance of our framework in the presence of mismatches can be predetermined.

cs.CV↗

arXiv2023

PASTA: Pessimistic Assortment Optimization

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

cs.LG↗

arXiv2023

Domain Adaptation via Rebalanced Sub-domain Alignment

Unsupervised domain adaptation (UDA) is a technique used to transfer knowledge from a labeled source domain to a different but related unlabeled target domain. While many UDA methods have shown success in the past, they often assume that the source and target domains must have identical class label distributions, which can limit their effectiveness in real-world scenarios. To address this limitation, we propose a novel generalization bound that reweights source classification error by aligning source and target sub-domains. We prove that our proposed generalization bound is at least as strong as existing bounds under realistic assumptions, and we empirically show that it is much stronger on real-world data. We then propose an algorithm to minimize this novel generalization bound. We demonstrate by numerical experiments that this approach improves performance in shifted class distribution scenarios compared to state-of-the-art methods.

cs.LG↗

arXiv2023

Quickest Change Detection for Unnormalized Statistical Models

Classical quickest change detection algorithms require modeling pre-change and post-change distributions. Such an approach may not be feasible for various machine learning models because of the complexity of computing the explicit distributions. Additionally, these methods may suffer from a lack of robustness to model mismatch and noise. This paper develops a new variant of the classical Cumulative Sum (CUSUM) algorithm for the quickest change detection. This variant is based on Fisher divergence and the Hyvärinen score and is called the Score-based CUSUM (SCUSUM) algorithm. The SCUSUM algorithm allows the applications of change detection for unnormalized statistical models, i.e., models for which the probability density function contains an unknown normalization constant. The asymptotic optimality of the proposed algorithm is investigated by deriving expressions for average detection delay and the mean running time to a false alarm. Numerical results are provided to demonstrate the performance of the proposed algorithm.

stat.ML↗

arXiv2022

Personalized Federated Recommender Systems with Private and Partially Federated AutoEncoders

Recommender Systems (RSs) have become increasingly important in many application domains, such as digital marketing. Conventional RSs often need to collect users' data, centralize them on the server-side, and form a global model to generate reliable recommendations. However, they suffer from two critical limitations: the personalization problem that the RSs trained traditionally may not be customized for individual users, and the privacy problem that directly sharing user data is not encouraged. We propose Personalized Federated Recommender Systems (PersonalFR), which introduces a personalized autoencoder-based recommendation model with Federated Learning (FL) to address these challenges. PersonalFR guarantees that each user can learn a personal model from the local dataset and other participating users' data without sharing local data, data embeddings, or models. PersonalFR consists of three main components, including AutoEncoder-based RSs (ARSs) that learn the user-item interactions, Partially Federated Learning (PFL) that updates the encoder locally and aggregates the decoder on the server-side, and Partial Compression (PC) that only computes and transmits active model parameters. Extensive experiments on two real-world datasets demonstrate that PersonalFR can achieve private and personalized performance comparable to that trained by centralizing all users' data. Moreover, PersonalFR requires significantly less computation and communication overhead than standard FL baselines.

cs.IR↗

arXiv2022

Characteristic Neural Ordinary Differential Equations

We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an ODE, C-NODE models the evolution of the latent variables as the solution of a family of first-order quasi-linear partial differential equations (PDEs) along curves on which the PDEs reduce to ODEs, referred to as characteristic curves. This in turn allows the application of the standard frameworks for solving ODEs, namely the adjoint method. Learning optimal characteristic curves for given tasks improves the performance and computational efficiency, compared to state of the art NODE models. We prove that the C-NODE framework extends the classical NODE on classification tasks by demonstrating explicit C-NODE representable functions not expressible by NODEs. Additionally, we present C-NODE-based continuous normalizing flows, which describe the density evolution of latent variables along multiple dimensions. Empirical results demonstrate the improvements provided by the proposed method for classification and density estimation on CIFAR-10, SVHN, and MNIST datasets under a similar computational budget as the existing NODE methods. The results also provide empirical evidence that the learned curves improve the efficiency of the system through a lower number of parameters and function evaluations compared with baselines.

cs.LG↗

arXiv2022

Decentralized Multi-Target Cross-Domain Recommendation for Multi-Organization Collaborations

Recommender Systems (RSs) are operated locally by different organizations in many realistic scenarios. If various organizations can fully share their data and perform computation in a centralized manner, they may significantly improve the accuracy of recommendations. However, collaborations among multiple organizations in enhancing the performance of recommendations are primarily limited due to the difficulty of sharing data and models. To address this challenge, we propose Decentralized Multi-Target Cross-Domain Recommendation (DMTCDR) with Multi-Target Assisted Learning (MTAL) and Assisted AutoEncoder (AAE). Our method can help multiple organizations collaboratively improve their recommendation performance in a decentralized manner without sharing sensitive assets. Consequently, it allows decentralized organizations to collaborate and form a community of shared interest. We conduct extensive experiments to demonstrate that the new method can significantly outperform locally trained RSs and mitigate the cold start problem.

cs.IR↗

arXiv2022

GAL: Gradient Assisted Learning for Decentralized Multi-Organization Collaborations

Collaborations among multiple organizations, such as financial institutions, medical centers, and retail markets in decentralized settings are crucial to providing improved service and performance. However, the underlying organizations may have little interest in sharing their local data, models, and objective functions. These requirements have created new challenges for multi-organization collaboration. In this work, we propose Gradient Assisted Learning (GAL), a new method for multiple organizations to assist each other in supervised learning tasks without sharing local data, models, and objective functions. In this framework, all participants collaboratively optimize the aggregate of local loss functions, and each participant autonomously builds its own model by iteratively fitting the gradients of the overarching objective function. We also provide asymptotic convergence analysis and practical case studies of GAL. Experimental studies demonstrate that GAL can achieve performance close to centralized learning when all data, models, and objective functions are fully disclosed.

cs.LG↗

arXiv2022

SemiFL: Semi-Supervised Federated Learning for Unlabeled Clients with Alternate Training

Federated Learning allows the training of machine learning models by using the computation and private data resources of many distributed clients. Most existing results on Federated Learning (FL) assume the clients have ground-truth labels. However, in many practical scenarios, clients may be unable to label task-specific data due to a lack of expertise or resource. We propose SemiFL to address the problem of combining communication-efficient FL such as FedAvg with Semi-Supervised Learning (SSL). In SemiFL, clients have completely unlabeled data and can train multiple local epochs to reduce communication costs, while the server has a small amount of labeled data. We provide a theoretical understanding of the success of data augmentation-based SSL methods to illustrate the bottleneck of a vanilla combination of communication-efficient FL with SSL. To address this issue, we propose alternate training to `fine-tune global model with labeled data' and `generate pseudo-labels with the global model.' We conduct extensive experiments and demonstrate that our approach significantly improves the performance of a labeled server with unlabeled clients training with multiple local epochs. Moreover, our method outperforms many existing SSFL baselines and performs competitively with the state-of-the-art FL and SSL results.

cs.LG↗

arXiv2022

Inference and Sampling for Archimax Copulas

Understanding multivariate dependencies in both the bulk and the tails of a distribution is an important problem for many applications, such as ensuring algorithms are robust to observations that are infrequent but have devastating effects. Archimax copulas are a family of distributions endowed with a precise representation that allows simultaneous modeling of the bulk and the tails of a distribution. Rather than separating the two as is typically done in practice, incorporating additional information from the bulk may improve inference of the tails, where observations are limited. Building on the stochastic representation of Archimax copulas, we develop a non-parametric inference method and sampling algorithm. Our proposed methods, to the best of our knowledge, are the first that allow for highly flexible and scalable inference and sampling algorithms, enabling the increased use of Archimax copulas in practical settings. We experimentally compare to state-of-the-art density modeling techniques, and the results suggest that the proposed method effectively extrapolates to the tails while scaling to higher dimensional data. Our findings suggest that the proposed algorithms can be used in a variety of applications where understanding the interplay between the bulk and the tails of a distribution is necessary, such as healthcare and safety.

stat.ME↗

arXiv2022

Multimodal Controller for Generative Models

Class-conditional generative models are crucial tools for data generation from user-specified class labels. Existing approaches for class-conditional generative models require nontrivial modifications of backbone generative architectures to model conditional information fed into the model. This paper introduces a plug-and-play module named `multimodal controller' to generate multimodal data without introducing additional learning parameters. In the absence of the controllers, our model reduces to non-conditional generative models. We test the efficacy of multimodal controllers on CIFAR10, COIL100, and Omniglot benchmark datasets. We demonstrate that multimodal controlled generative models (including VAE, PixelCNN, Glow, and GAN) can generate class-conditional images of significantly better quality when compared with conditional generative models. Moreover, we show that multimodal controlled models can also create novel modalities of images.

cs.LG↗

arXiv2022

Fisher Task Distance and Its Application in Neural Architecture Search

We formulate an asymmetric (or non-commutative) distance between tasks based on Fisher Information Matrices, called Fisher task distance. This distance represents the complexity of transferring the knowledge from one task to another. We provide a proof of consistency for our distance through theorems and experiments on various classification tasks from MNIST, CIFAR-10, CIFAR-100, ImageNet, and Taskonomy datasets. Next, we construct an online neural architecture search framework using the Fisher task distance, in which we have access to the past learned tasks. By using the Fisher task distance, we can identify the closest learned tasks to the target task, and utilize the knowledge learned from these related tasks for the target task. Here, we show how the proposed distance between a target task and a set of learned tasks can be used to reduce the neural architecture search space for the target task. The complexity reduction in search space for task-specific architectures is achieved by building on the optimized architectures for similar tasks instead of doing a full search and without using this side information. Experimental results for tasks in MNIST, CIFAR-10, CIFAR-100, ImageNet datasets demonstrate the efficacy of the proposed approach and its improvements, in terms of the performance and the number of parameters, over other gradient-based search methods, such as ENAS, DARTS, PC-DARTS.

cs.LG↗

arXiv2022

Semi-Empirical Objective Functions for MCMC Proposal Optimization

Current objective functions used for training neural MCMC proposal distributions implicitly rely on architectural restrictions to yield sensible optimization results, which hampers the development of highly expressive neural MCMC proposal architectures. In this work, we introduce and demonstrate a semi-empirical procedure for determining approximate objective functions suitable for optimizing arbitrarily parameterized proposal distributions in MCMC methods. Our proposed Ab Initio objective functions consist of the weighted combination of functions following constraints on their global optima and transformation invariances that we argue should be upheld by general measures of MCMC efficiency for use in proposal optimization. Our experimental results demonstrate that Ab Initio objective functions maintain favorable performance and preferable optimization behavior compared to existing objective functions for neural MCMC optimization. We find that Ab Initio objective functions are sufficiently robust to enable the confident optimization of neural proposal distributions parameterized by deep generative networks extending beyond the regimes of traditional MCMC schemes

cs.LG↗

arXiv2022

Toward Data-Driven STAP Radar

Using an amalgamation of techniques from classical radar, computer vision, and deep learning, we characterize our ongoing data-driven approach to space-time adaptive processing (STAP) radar. We generate a rich example dataset of received radar signals by randomly placing targets of variable strengths in a predetermined region using RFView, a site-specific radio frequency modeling and simulation tool developed by ISL Inc. For each data sample within this region, we generate heatmap tensors in range, azimuth, and elevation of the output power of a minimum variance distortionless response (MVDR) beamformer, which can be replaced with a desired test statistic. These heatmap tensors can be thought of as stacked images, and in an airborne scenario, the moving radar creates a sequence of these time-indexed image stacks, resembling a video. Our goal is to use these images and videos to detect targets and estimate their locations, a procedure reminiscent of computer vision algorithms for object detection$-$namely, the Faster Region-Based Convolutional Neural Network (Faster R-CNN). The Faster R-CNN consists of a proposal generating network for determining regions of interest (ROI), a regression network for positioning anchor boxes around targets, and an object classification algorithm; it is developed and optimized for natural images. Our ongoing research will develop analogous tools for heatmap images of radar data. In this regard, we will generate a large, representative adaptive radar signal processing database for training and testing, analogous in spirit to the COCO dataset for natural images. As a preliminary example, we present a regression network in this paper for estimating target locations to demonstrate the feasibility of and significant improvements provided by our data-driven approach.

cs.CV↗

arXiv2022

Modeling Extremes with d-max-decreasing Neural Networks

We propose a novel neural network architecture that enables non-parametric calibration and generation of multivariate extreme value distributions (MEVs). MEVs arise from Extreme Value Theory (EVT) as the necessary class of models when extrapolating a distributional fit over large spatial and temporal scales based on data observed in intermediate scales. In turn, EVT dictates that $d$-max-decreasing, a stronger form of convexity, is an essential shape constraint in the characterization of MEVs. As far as we know, our proposed architecture provides the first class of non-parametric estimators for MEVs that preserve these essential shape constraints. We show that our architecture approximates the dependence structure encoded by MEVs at parametric rate. Moreover, we present a new method for sampling high-dimensional MEVs using a generative model. We demonstrate our methodology on a wide range of experimental settings, ranging from environmental sciences to financial mathematics and verify that the structural properties of MEVs are retained compared to existing methods.

stat.ML↗