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Hamid Usefi

Publications and source records attributed to Hamid Usefi.

At least 19 recordsLinked to original sources
arXiv2026

Cross-Dataset Generalization in Breast MRI Tumor Classification via Class-Wise Dataset Mixing

Breast MRI is highly sensitive for detecting breast tumors, but exams contain many slices and require substantial reading time. Deep learning models often perform well on internal splits but can fail across institutions because of domain shift and dataset-origin bias. We study this failure mode for binary breast MRI tumor classification. EfficientNet-B3 and WaveViT-Small are trained using Duke Breast Cancer MRI and fastMRI, and evaluated only on the independent multi-center MAMA-MIA cohort. In a deliberately confounded setup, where label is perfectly correlated with dataset origin, external accuracy is near chance (0.5048--0.5265), despite very high recall. We then construct a mixed training set in which each class contains samples from both Duke and fastMRI, while preserving patient-level splitting, augmentation, and leakage controls. On MAMA-MIA, dataset mixing improves accuracy/F1 to 0.8463/0.8625 for WaveViT-Small and 0.8884/0.8994 for EfficientNet-B3. These results show that controlling dataset-origin bias is important for reliable breast MRI classification.

cs.CV↗
arXiv2023

Assessing the Reproducibility of Machine-learning-based Biomarker Discovery in Parkinson's Disease

Genome-Wide Association Studies (GWAS) help identify genetic variations in people with diseases such as Parkinson's disease (PD), which are less common in those without the disease. Thus, GWAS data can be used to identify genetic variations associated with the disease. Feature selection and machine learning approaches can be used to analyze GWAS data and identify potential disease biomarkers. However, GWAS studies have technical variations that affect the reproducibility of identified biomarkers, such as differences in genotyping platforms and selection criteria for individuals to be genotyped. To address this issue, we collected five GWAS datasets from the database of Genotypes and Phenotypes (dbGaP) and explored several data integration strategies. We evaluated the agreement among different strategies in terms of the Single Nucleotide Polymorphisms (SNPs) that were identified as potential PD biomarkers. Our results showed a low concordance of biomarkers discovered using different datasets or integration strategies. However, we identified fifty SNPs that were identified at least twice, which could potentially serve as novel PD biomarkers. These SNPs are indirectly linked to PD in the literature but have not been directly associated with PD before. These findings open up new potential avenues of investigation.

q-bio.GN↗
arXiv2022

Unsupervised Liu-type Shrinkage Estimators for Mixture of Regression Models

In many applications (e.g., medical studies), the population of interest (e.g., disease status) comprises heterogeneous subpopulations. The mixture of probabilistic regression models is one of the most common techniques to incorporate the information of covariates into learning of the population heterogeneity. Despite its flexibility, the model may lead to unreliable estimates in the presence of multicollinearity problem. In this paper, we develop Liu-type shrinkage methods through an unsupervised learning approach to estimate the model coefficients in multicollinearity. The performance of the developed methods is evaluated via classification and stochastic versions of EM algorithms. The numerical studies show that the proposed methods outperform their Ridge and maximum likelihood counterparts. Finally, the developed methods are applied to analyze the bone mineral data of women aged 50 and older.

stat.ME↗
arXiv2022

Liu-type Shrinkage Estimators for Mixture of Logistic Regressions: An Osteoporosis Study

The logistic regression model is one of the most powerful statistical methods for the analysis of binary data. The logistic regression allows to use a set of covariates to explain the binary responses. The mixture of logistic regression models is used to fit heterogeneous populations through an unsupervised learning approach. The multicollinearity problem is one of the most common problems in logistics and a mixture of logistic regressions where the covariates are highly correlated. This problem results in unreliable maximum likelihood estimates for the regression coefficients. This research developed shrinkage methods to deal with the multicollinearity in a mixture of logistic regression models. These shrinkage methods include ridge and Liu-type estimators. Through extensive numerical studies, we show that the developed methods provide more reliable results in estimating the coefficients of the mixture. Finally, we applied the shrinkage methods to analyze the bone disorder status of women aged 50 and older.

stat.ME↗
arXiv2020

Clustering, multicollinearity, and singular vectors

Let $A$ be a matrix with its pseudo-matrix $A^{\dagger}$ and set $S=I-A^{\dagger}A$. We prove that, after re-ordering the columns of $A$, the matrix $S$ has a block-diagonal form where each block corresponds to a set of linearly dependent columns. This allows us to identify redundant columns in $A$. We explore some applications in supervised and unsupervised learning, specially feature selection, clustering, and sensitivity of solutions of least squares solutions.

cs.LG↗
arXiv2020

Detecting ulcerative colitis from colon samples using efficient feature selection and machine learning

Ulcerative colitis (UC) is one of the most common forms of inflammatory bowel disease (IBD) characterized by inflammation of the mucosal layer of the colon. Diagnosis of UC is based on clinical symptoms, and then confirmed based on endoscopic, histologic and laboratory findings. Feature selection and machine learning have been previously used for creating models to facilitate the diagnosis of certain diseases. In this work, we used a recently developed feature selection algorithm (DRPT) combined with a support vector machine (SVM) classifier to generate a model to discriminate between healthy subjects and subjects with UC based on the expression values of 32 genes in colon samples. We validated our model with an independent gene expression dataset of colonic samples from subjects in active and inactive periods of UC. Our model perfectly detected all active cases and had an average precision of 0.62 in the inactive cases. Compared with results reported in previous studies and a model generated by a recently published software for biomarker discovery using machine learning (BioDiscML), our final model for detecting UC shows better performance in terms of average precision.

q-bio.QM↗
arXiv2020

Solvability of Poisson algebras

Let $P$ be a Poisson algebra with a Lie bracket $\{, \}$ over a field $\F$ of characteristic $p\geq 0$. In this paper, the Lie structure of $P$ is investigated. In particular, if $P$ is solvable with respect to its Lie bracket, then we prove that the Poisson ideal $\mathcal{J}$ of $P$ generated by all elements $\{\{\{x_1, x_2\}, \{x_3, x_4\}\}, x_5\}$ with $x_1,\ldots ,x_5 \in P$ is associative nilpotent of index bounded by a function of the derived length of $P$. We use this result to further prove that if $P$ is solvable and $p\neq 2$, then the Poisson ideal $\{P,P\}P$ is nil.

math.RA↗
arXiv2020

High-Dimensional Feature Selection for Genomic Datasets

A central problem in machine learning and pattern recognition is the process of recognizing the most important features. In this paper, we provide a new feature selection method (DRPT) that consists of first removing the irrelevant features and then detecting correlations between the remaining features. Let $D=[A\mid \mathbf{b}]$ be a dataset, where $\mathbf{b}$ is the class label and $A$ is a matrix whose columns are the features. We solve $A\mathbf{x} = \mathbf{b}$ using the least squares method and the pseudo-inverse of $A$. Each component of $\mathbf{x}$ can be viewed as an assigned weight to the corresponding column (feature). We define a threshold based on the local maxima of $\mathbf{x}$ and remove those features whose weights are smaller than the threshold. To detect the correlations in the reduced matrix, which we still call $A$, we consider a perturbation $\tilde A$ of $A$. We prove that correlations are encoded in $\Delta\mathbf{x}=\mid \mathbf{x} -\tilde{\mathbf{x}}\mid $, where $\tilde{\mathbf{x}}$ is the least quares solution of $\tilde A\tilde{\mathbf{x}}=\mathbf{b}$. We cluster features first based on $\Delta\mathbf{x}$ and then using the entropy of features. Finally, a feature is selected from each sub-cluster based on its weight and entropy. The effectiveness of DRPT has been verified by performing a series of comparisons with seven state-of-the-art feature selection methods over ten genetic datasets ranging up from 9,117 to 267,604 features. The results show that, over all, the performance of DRPT is favorable in several aspects compared to each feature selection algorithm. \e

cs.LG↗
arXiv2019

The isomorphism problem for universal enveloping algebras of four-dimensional solvable Lie algebras

This paper is a contribution to the isomorphism problem for universal enveloping algebras of finite-dimensional Lie algebras. We focus on solvable Lie algebras of small dimensions over fields of arbitrary characteristic. We prove, over an arbitrary field, that the isomorphism type of a metabelian Lie algebra whose derived subalgebra has codimension one is determined by its universal enveloping algebra. As an application of the results in this paper, we solve the isomorphism problem for solvable Lie algebras of dimension four over fields of characteristic zero and also point out the problems that occur in prime characteristic.

math.RA↗
arXiv2019

A Feature Selection Based on Perturbation Theory

Consider a supervised dataset $D=[A\mid \textbf{b}]$, where $\textbf{b}$ is the outcome column, rows of $D$ correspond to observations, and columns of $A$ are the features of the dataset. A central problem in machine learning and pattern recognition is to select the most important features from $D$ to be able to predict the outcome. In this paper, we provide a new feature selection method where we use perturbation theory to detect correlations between features. We solve $AX=\textbf{b}$ using the method of least squares and singular value decomposition of $A$. In practical applications, such as in bioinformatics, the number of rows of $A$ (observations) are much less than the number of columns of $A$ (features). So we are dealing with singular matrices with big condition numbers. Although it is known that the solutions of least square problems in singular case are very sensitive to perturbations in $A$, our novel approach in this paper is to prove that the correlations between features can be detected by applying perturbations to $A$. The effectiveness of our method is verified by performing a series of comparisons with conventional and novel feature selection methods in the literature. It is demonstrated that in most situations, our method chooses considerably less number of features while attaining or exceeding the accuracy of the other methods.

cs.LG↗
arXiv2017

Enveloping algebras that are principal ideal rings

Let $L$ be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of $L$ is a principal ideal ring if and only if $L$ is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.

math.RA↗
arXiv2016

Perfect and semiperfect restricted enveloping algebras

For a restricted Lie algebra $L$, the conditions under which its restricted enveloping algebra $u(L)$ is semiperfect are investigated. Moreover, it is proved that $u(L)$ is left (or right) perfect if and only if $L$ is finite-dimensional.

math.RA↗
arXiv2016

Homomorphic Evaluation of Database Queries

Homomorphic encryption is an encryption method that enables computing over encrypted data. This has a wide range of real world ramifications such as being able to blindly compute a search result sent to a remote server without revealing its content. This paper discusses how database search queries can be made secure using a homomorphic encryption scheme. We propose a new database search technique that can be used with the ring-based fully homomorphic encryption scheme proposed by Braserski.

cs.CR↗
arXiv2015

Engel condition on enveloping algebras of lie superalgebras

Let L be a Lie superalgebra over a fled of characteristic p\neq 2 with enveloping algebra U(L) or let L be a restricted Lie superalgebra over a field of characteristic p > 2 with restricted enveloping algebra u(L). In this note, we establish when u(L) or U(L) is bounded Lie Engel.

math.RA↗
arXiv2015

Lie Properties of Restricted Enveloping Algebras

Let L be a restricted Lie algebra over a field of positive characteristic. We survey the known results about the Lie structure of the restricted enveloping algebra u(L) of L. Related results about the structure of the group of units and the symmetric and skew-symmetric elements of u(L) are also discussed. Moreover, a new theorem about an upper bound for the Lie nilpotency class of u(L) is proved.

math.RA↗
arXiv2014

Classification of 5-dimensional restricted Lie algebras over perfect fields, I

The purpose of this paper is to classify all $p$-nilpotent restricted Lie algebras of dimension 5 over perfect fields of characteristic $p\geq 5$. Our work builds upon the recent work of Schneider and Usefi on the classification of $p$-nilpotent restricted Lie algebras of dimension up to 4 over perfect fields of characteristic $p$. The method we use here to classify $p$-nilpotent restricted Lie algebras is the analogue of Skjelbred-Sund method for classifying nilpotent Lie algebras.

math.RA↗
arXiv2014

A note on diagonal and Hermitian surfaces

Aspects of the properties, enumeration and construction of points on diagonal and Hermitian surfaces have been considered extensively in the literature and are further considered here. The zeta function of diagonal surfaces is given as a direct result of the work of Wolfmann. Recursive construction techniques for the set of rational points of Hermitian surfaces are of interest. The relationship of these techniques here to the construction of codes on surfaces is briefly noted.

cs.IT↗