arXiv subjects

Seyed Abolfazl Motahari

Publications and source records attributed to Seyed Abolfazl Motahari.

17 recordsLinked to original sources

arXiv2024

Efficient learning of differential network in multi-source non-paranormal graphical models

This paper addresses learning of sparse structural changes or differential network between two classes of non-paranormal graphical models. We assume a multi-source and heterogeneous dataset is available for each class, where the covariance matrices are identical for all non-paranormal graphical models. The differential network, which are encoded by the difference precision matrix, can then be decoded by optimizing a lasso penalized D-trace loss function. To this aim, an efficient approach is proposed that outputs the exact solution path, outperforming the previous methods that only sample from the solution path in pre-selected regularization parameters. Notably, our proposed method has low computational complexity, especially when the differential network are sparse. Our simulations on synthetic data demonstrate a superior performance for our strategy in terms of speed and accuracy compared to an existing method. Moreover, our strategy in combining datasets from multiple sources is shown to be very effective in inferring differential network in real-world problems. This is backed by our experimental results on drug resistance in tumor cancers. In the latter case, our strategy outputs important genes for drug resistance which are already confirmed by various independent studies.

cs.LG↗

arXiv2023

Sample Complexity Bounds for Learning High-dimensional Simplices in Noisy Regimes

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a $\ell_2$ distance of at most $\varepsilon$ from the true simplex (for any $\varepsilon>0$). Also, we theoretically show that in order to achieve this bound, it is sufficient to have $n\ge\left(K^2/\varepsilon^2\right)e^{Ω\left(K/\mathrm{SNR}^2\right)}$ samples, where $\mathrm{SNR}$ stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as $\mathrm{SNR}\geΩ\left(K^{1/2}\right)$, the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in \citep{ashtiani2018nearly}, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

stat.ML↗

arXiv2023

Isoform Function Prediction Using a Deep Neural Network

Isoforms are mRNAs produced from the same gene site in the phenomenon called Alternative Splicing. Studies have shown that more than 95% of human multi-exon genes have undergone alternative splicing. Although there are few changes in mRNA sequence, They may have a systematic effect on cell function and regulation. It is widely reported that isoforms of a gene have distinct or even contrasting functions. Most studies have shown that alternative splicing plays a significant role in human health and disease. Despite the wide range of gene function studies, there is little information about isoforms' functionalities. Recently, some computational methods based on Multiple Instance Learning have been proposed to predict isoform function using gene function and gene expression profile. However, their performance is not desirable due to the lack of labeled training data. In addition, probabilistic models such as Conditional Random Field (CRF) have been used to model the relation between isoforms. This project uses all the data and valuable information such as isoform sequences, expression profiles, and gene ontology graphs and proposes a comprehensive model based on Deep Neural Networks. The UniProt Gene Ontology (GO) database is used as a standard reference for gene functions. The NCBI RefSeq database is used for extracting gene and isoform sequences, and the NCBI SRA database is used for expression profile data. Metrics such as Receiver Operating Characteristic Area Under the Curve (ROC AUC) and Precision-Recall Under the Curve (PR AUC) are used to measure the prediction accuracy.

q-bio.GN↗

arXiv2021

Distributed Sparse Feature Selection in Communication-Restricted Networks

This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations from an unknown sparse linear model. However, the presumed training set which includes $n$ data samples in $\mathbb{R}^p$ is already distributed over a large network with $N$ clients connected through extremely low-bandwidth links. Also, we consider the asymptotic configuration of $1\ll N\ll n\ll p$. In order to infer the causal dimensions from the whole dataset, we propose a simple, yet effective method for information sharing in the network. In this regard, we theoretically show that the true causal features can be reliably recovered with negligible bandwidth usage of $O\left(N\log p\right)$ across the network. This yields a significantly lower communication cost in comparison with the trivial case of transmitting all the samples to a single node (centralized scenario), which requires $O\left(np\right)$ transmissions. Even more sophisticated schemes such as ADMM still have a communication complexity of $O\left(Np\right)$. Surprisingly, our sample complexity bound is proved to be the same (up to a constant factor) as the optimal centralized approach for a fixed performance measure in each node, while that of a naïve decentralized technique grows linearly with $N$. Theoretical guarantees in this paper are based on the recent analytic framework of debiased LASSO in Javanmard et al. (2019), and are supported by several computer experiments performed on both synthetic and real-world datasets.

stat.ML↗

arXiv2020

Regularizing Recurrent Neural Networks via Sequence Mixup

In this paper, we extend a class of celebrated regularization techniques originally proposed for feed-forward neural networks, namely Input Mixup (Zhang et al., 2017) and Manifold Mixup (Verma et al., 2018), to the realm of Recurrent Neural Networks (RNN). Our proposed methods are easy to implement and have a low computational complexity, while leverage the performance of simple neural architectures in a variety of tasks. We have validated our claims through several experiments on real-world datasets, and also provide an asymptotic theoretical analysis to further investigate the properties and potential impacts of our proposed techniques. Applying sequence mixup to BiLSTM-CRF model (Huang et al., 2015) to Named Entity Recognition task on CoNLL-2003 data (Sang and De Meulder, 2003) has improved the F-1 score on the test stage and reduced the loss, considerably.

cs.CL↗

arXiv2020

The Capacity of Associated Subsequence Retrieval

The objective of a genome-wide association study (GWAS) is to associate subsequences of individuals' genomes to the observable characteristics called phenotypes (e.g., high blood pressure). Motivated by the GWAS problem, in this paper we introduce the information-theoretic problem of \emph{associated subsequence retrieval}, where a dataset of $N$ (possibly high-dimensional) sequences of length $G$, and their corresponding observable (binary) characteristics is given. The sequences are chosen independently and uniformly at random from $\mathcal{X}^G$, where $\mathcal{X}$ is a finite alphabet. The observable (binary) characteristic is only related to a specific unknown subsequence of length $L$ of the sequences, called \textit{associated subsequence}. For each sequence, if the associated subsequence of it belongs to a universal finite set, then it is more likely to display the observable characteristic (i.e., it is more likely that the observable characteristic is one). The goal is to retrieve the associated subsequence using a dataset of $N$ sequences and their observable characteristics. We demonstrate that as the parameters $N$, $G$, and $L$ grow, a threshold effect appears in the curve of probability of error versus the rate which is defined as ${Gh(L/G)}/{N}$, where $h(\cdot)$ is the binary entropy function. This effect allows us to define the capacity of associated subsequence retrieval. We develop an achievable scheme and a matching converse for this problem, and thus characterize its capacity in two scenarios: the zero-error-rate and the $ε$-error-rate.

cs.IT↗

arXiv2020

On Statistical Learning of Simplices: Unmixing Problem Revisited

We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of `spectral unmixing'. We theoretically show that a sufficient sample complexity for reliable learning of a $K$-dimensional simplex up to a total-variation error of $ε$ is $O\left(\frac{K^2}ε\log\frac{K}ε\right)$, which yields a substantial improvement over existing bounds. Based on our new theoretical framework, we also propose a heuristic approach for the inference of simplices. Experimental results on synthetic and real-world datasets demonstrate a comparable performance for our method on noiseless samples, while we outperform the state-of-the-art in noisy cases.

cs.LG↗

arXiv2019

Private Shotgun DNA Sequencing: A Structured Approach

DNA sequencing has faced a huge demand since it was first introduced as a service to the public. This service is often offloaded to the sequencing companies who will have access to full knowledge of individuals' sequences, a major violation of privacy. To address this challenge, we propose a solution, which is based on separating the process of reading the fragments of sequences, which is done at a sequencing machine, and assembling the reads, which is done at a trusted local data collector. To confuse the sequencer, in a pooled sequencing scenario, in which multiple sequences are going to be sequenced simultaneously, for each target individual, we add fragments of one non-target individual, with a known DNA sequence at the data collector. Then coverage depth of the individuals, defined as the number of DNA fragments per DNA site, are selected proportional to the powers of two. This layered structured solution allows us to ensure privacy, using only one sequencing machine, in contrast to our previous solution, where we relied on the existence of multiple non-colluding sequencing machines.

cs.IT↗

arXiv2018

Structure Learning of Sparse GGMs over Multiple Access Networks

A central machine is interested in estimating the underlying structure of a sparse Gaussian Graphical Model (GGM) from datasets distributed across multiple local machines. The local machines can communicate with the central machine through a wireless multiple access channel. In this paper, we are interested in designing effective strategies where reliable learning is feasible under power and bandwidth limitations. Two approaches are proposed: Signs and Uncoded methods. In Signs method, the local machines quantize their data into binary vectors and an optimal channel coding scheme is used to reliably send the vectors to the central machine where the structure is learned from the received data. In Uncoded method, data symbols are scaled and transmitted through the channel. The central machine uses the received noisy symbols to recover the structure. Theoretical results show that both methods can recover the structure with high probability for large enough sample size. Experimental results indicate the superiority of Signs method over Uncoded method under several circumstances.

cs.LG↗

arXiv2018

Information Theoretic Bounds on Optimal Worst-case Error in Binary Mixture Identification

Identification of latent binary sequences from a pool of noisy observations has a wide range of applications in both statistical learning and population genetics. Each observed sequence is the result of passing one of the latent mother-sequences through a binary symmetric channel, which makes this configuration analogous to a special case of Bernoulli Mixture Models. This paper aims to attain an asymptotically tight upper-bound on the error of Maximum Likelihood mixture identification in such problems. The obtained results demonstrate fundamental guarantees on the inference accuracy of the optimal estimator. To this end, we set out to find the closest pair of discrete distributions with respect to the Chernoff Information measure. We provide a novel technique to lower bound the Chernoff Information in an efficient way. We also show that a drastic phase transition occurs at noise level 0.25. Our findings reveal that the identification problem becomes much harder as the noise probability exceeds this threshold.

math.ST↗

arXiv2018

Private Shotgun DNA Sequencing

Current techniques in sequencing a genome allow a service provider (e.g. a sequencing company) to have full access to the genome information, and thus the privacy of individuals regarding their lifetime secret is violated. In this paper, we introduce the problem of private DNA sequencing, where the goal is to keep the DNA sequence private to the sequencer. We propose an architecture, where the task of reading fragments of DNA and the task of DNA assembly are separated, the former is done at the sequencer(s), and the later is completed at a local trusted data collector. To satisfy the privacy constraint at the sequencer and reconstruction condition at the data collector, we create an information gap between these two relying on two techniques: (i) we use more than one non-colluding sequencer, all reporting the read fragments to the single data collector, (ii) adding the fragments of some known DNA molecules, which are still unknown to the sequencers, to the pool. We prove that these two techniques provide enough freedom to satisfy both conditions at the same time.

q-bio.GN↗

arXiv2018

Learning of Tree-Structured Gaussian Graphical Models on Distributed Data under Communication Constraints

In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messages from the other nodes. We present a set of communication efficient strategies, which are theoretically proved to convey sufficient information for reliable learning of the structure. In particular, our analyses show that even if each machine sends only the signs of its local data samples to the central node, the tree structure can still be recovered with high accuracy. Our simulation results on both synthetic and real-world datasets show that our strategies achieve a desired accuracy in inferring the underlying structure, while spending a small budget on communication.

cs.LG↗

arXiv2018

On the Identifiability of Finite Mixtures of Finite Product Measures

The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with cardinality $M$.The variables are independent in each mixture component. The identifiability of a mixture model means the possibility of attaining the mixture components parameters by observing its mixture distribution. In this paper, we investigate fundamental relations between the identifiability of mixture models and the separability of their observed variables by introducing two types of separability: strongly and weakly separable variables. Roughly speaking, a variable is said to be separable, if and only if it has some differences among its probability distributions in different mixture components. We prove that mixture models are identifiable if the number of strongly separable variables is greater than or equal to $2K-1$, independent form $M$. This fundamental threshold is shown to be tight, where a family of non-identifiable mixture models with less than $2K-1$ strongly separable variables is provided. We also show that mixture models are identifiable if they have at least $2K$ weakly separable variables. To prove these theorems, we introduce a particular polynomial, called characteristic polynomial, which translates the identifiability conditions to identity of polynomials and allows us to construct an inductive proof.

math.ST↗

arXiv2018

Cell Identity Codes: Understanding Cell Identity from Gene Expression Profiles using Deep Neural Networks

Understanding cell identity is an important task in many biomedical areas. Expression patterns of specific marker genes have been used to characterize some limited cell types, but exclusive markers are not available for many cell types. A second approach is to use machine learning to discriminate cell types based on the whole gene expression profiles (GEPs). The accuracies of simple classification algorithms such as linear discriminators or support vector machines are limited due to the complexity of biological systems. We used deep neural networks to analyze 1040 GEPs from 16 different human tissues and cell types. After comparing different architectures, we identified a specific structure of deep autoencoders that can encode a GEP into a vector of 30 numeric values, which we call the cell identity code (CIC). The original GEP can be reproduced from the CIC with an accuracy comparable to technical replicates of the same experiment. Although we use an unsupervised approach to train the autoencoder, we show different values of the CIC are connected to different biological aspects of the cell, such as different pathways or biological processes. This network can use CIC to reproduce the GEP of the cell types it has never seen during the training. It also can resist some noise in the measurement of the GEP. Furthermore, we introduce classifier autoencoder, an architecture that can accurately identify cell type based on the GEP or the CIC.

q-bio.GN↗

arXiv2017

Learning of Gaussian Processes in Distributed and Communication Limited Systems

It is of fundamental importance to find algorithms obtaining optimal performance for learning of statistical models in distributed and communication limited systems. Aiming at characterizing the optimal strategies, we consider learning of Gaussian Processes (GPs) in distributed systems as a pivotal example. We first address a very basic problem: how many bits are required to estimate the inner-products of Gaussian vectors across distributed machines? Using information theoretic bounds, we obtain an optimal solution for the problem which is based on vector quantization. Two suboptimal and more practical schemes are also presented as substitute for the vector quantization scheme. In particular, it is shown that the performance of one of the practical schemes which is called per-symbol quantization is very close to the optimal one. Schemes provided for the inner-product calculations are incorporated into our proposed distributed learning methods for GPs. Experimental results show that with spending few bits per symbol in our communication scheme, our proposed methods outperform previous zero rate distributed GP learning schemes such as Bayesian Committee Model (BCM) and Product of experts (PoE).

stat.ML↗

arXiv2016

Fundamental Limits of Pooled-DNA Sequencing

In this paper, fundamental limits in sequencing of a set of closely related DNA molecules are addressed. This problem is called pooled-DNA sequencing which encompasses many interesting problems such as haplotype phasing, metageomics, and conventional pooled-DNA sequencing in the absence of tagging. From an information theoretic point of view, we have proposed fundamental limits on the number and length of DNA reads in order to achieve a reliable assembly of all the pooled DNA sequences. In particular, pooled-DNA sequencing from both noiseless and noisy reads are investigated in this paper. In the noiseless case, necessary and sufficient conditions on perfect assembly are derived. Moreover, asymptotically tight lower and upper bounds on the error probability of correct assembly are obtained under a biologically plausible probabilistic model. For the noisy case, we have proposed two novel DNA read denoising methods, as well as corresponding upper bounds on assembly error probabilities. It has been shown that, under mild circumstances, the performance of the reliable assembly converges to that of the noiseless regime when, for a given read length, the number of DNA reads is sufficiently large. Interestingly, the emergence of long DNA read technologies in recent years envisions the applicability of our results in real-world applications.

cs.IT↗

arXiv2015

Multi-Server Coded Caching

In this paper, we consider multiple cache-enabled clients connected to multiple servers through an intermediate network. We design several topology-aware coding strategies for such networks. Based on topology richness of the intermediate network, and types of coding operations at internal nodes, we define three classes of networks, namely, dedicated, flexible, and linear networks. For each class, we propose an achievable coding scheme, analyze its coding delay, and also, compare it with an information theoretic lower bound. For flexible networks, we show that our scheme is order-optimal in terms of coding delay and, interestingly, the optimal memory-delay curve is achieved in certain regimes. In general, our results suggest that, in case of networks with multiple servers, type of network topology can be exploited to reduce service delay.

cs.IT↗