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Source author record

Damian Brzyski

Damian Brzyski appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Machine Learningmath.OCMethodologyComputationComputation and Languagemath.NAmath.STNumerical AnalysisStatistics Theory

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Published work

5 published item(s)

preprint2026arXiv

Is Textual Similarity Invariant under Machine Translation? Evidence Based on the Political Manifesto Corpus

We investigate the extent to which cosine similarity between paragraph embeddings is invariant under machine translation, using the Manifesto Corpus of over 2,800 political party platforms in 28 languages translated to English via the EU eTranslation service. Rather than measuring translation-induced semantic shift directly we measure the stability of pairwise similarity relationships across embedding models, and use inter-model disagreement on original-language text as a calibrated invariance threshold. This yields a per-language non-inferiority test for four hypotheses about how translation interacts with embedding choice, with verdicts that distinguish languages where translation demonstrably preserves semantic structure from those where it demonstrably degrades it and from those where the available evidence does not resolve the question. The framework is corpus- and pipeline-agnostic and extends naturally to downstream tasks. Applied to our data, it identifies ten languages with translation invariance and four with detectable distortion.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A Sparsity Inducing Nuclear-Norm Estimator (SpINNEr) for Matrix-Variate Regression in Brain Connectivity Analysis

Classical scalar-response regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. In medical applications, however, regressors are often in a form of multi-dimensional arrays. For example, one may be interested in using MRI imaging to identify which brain regions are associated with a health outcome. Vectorizing the two-dimensional image arrays is an unsatisfactory approach since it destroys the inherent spatial structure of the images and can be computationally challenging. We present an alternative approach - regularized matrix regression - where the matrix of regression coefficients is defined as a solution to the specific optimization problem. The method, called SParsity Inducing Nuclear Norm EstimatoR (SpINNEr), simultaneously imposes two penalty types on the regression coefficient matrix---the nuclear norm and the lasso norm---to encourage a low rank matrix solution that also has entry-wise sparsity. A specific implementation of the alternating direction method of multipliers (ADMM) is used to build a fast and efficient numerical solver. Our simulations show that SpINNEr outperforms other methods in estimation accuracy when the response-related entries (representing the brain's functional connectivity) are arranged in well-connected communities. SpINNEr is applied to investigate associations between HIV-related outcomes and functional connectivity in the human brain.

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preprint2016arXiv

Fast Saddle-Point Algorithm for Generalized Dantzig Selector and FDR Control with the Ordered l1-Norm

In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optimal $O(1/k)$ rate of convergence. Compared to the optimal non-SP algorithms, ours do not require specification of sensitive parameters that affect algorithm performance or solution quality. We also provide a new analysis showing a possibility of local acceleration to achieve the rate of $O(1/k^2)$ in special cases even without strong convexity or strong smoothness. As an application, we propose a GDS equipped with the ordered $\ell_1$-norm, showing its false discovery rate control properties in variable selection. Algorithm performance is compared between ours and other alternatives, including the linearized ADMM, Nesterov's smoothing, Nemirovski's mirror-prox, and the accelerated hybrid proximal extragradient techniques.

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preprint2016arXiv

Group SLOPE - adaptive selection of groups of predictors

Sorted L-One Penalized Estimation (SLOPE) is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation when one aims at selecting whole groups of explanatory variables instead of single regressors. Such groups can be formed by clustering strongly correlated predictors or groups of dummy variables corresponding to different levels of the same qualitative predictor. We formulate the respective convex optimization problem, gSLOPE (group SLOPE), and propose an efficient algorithm for its solution. We also define a notion of the group false discovery rate (gFDR) and provide a choice of the sequence of tuning parameters for gSLOPE so that gFDR is provably controlled at a prespecified level if the groups of variables are orthogonal to each other. Moreover, we prove that the resulting procedure adapts to unknown sparsity and is asymptotically minimax with respect to the estimation of the proportions of variance of the response variable explained by regressors from different groups. We also provide a method for the choice of the regularizing sequence when variables in different groups are not orthogonal but statistically independent and illustrate its good properties with computer simulations. Finally, we illustrate the advantages of gSLOPE in the context of Genome Wide Association Studies. R package grpSLOPE with implementation of our method is available on CRAN.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Group SLOPE - adaptive selection of groups of predictors

Sorted L-One Penalized Estimation is a relatively new convex optimization procedure which allows for adaptive selection of regressors under sparse high dimensional designs. Here we extend the idea of SLOPE to deal with the situation when one aims at selecting whole groups of explanatory variables instead of single regressors. This approach is particularly useful when variables in the same group are strongly correlated and thus true predictors are difficult to distinguish from their correlated "neighbors"'. We formulate the respective convex optimization problem, gSLOPE (group SLOPE), and propose an efficient algorithm for its solution. We also define a notion of the group false discovery rate (gFDR) and provide a choice of the sequence of tuning parameters for gSLOPE so that gFDR is provably controlled at a prespecified level if the groups of variables are orthogonal to each other. Moreover, we prove that the resulting procedure adapts to unknown sparsity and is asymptotically minimax with respect to the estimation of the proportions of variance of the response variable explained by regressors from different groups. We also provide a method for the choice of the regularizing sequence when variables in different groups are not orthogonal but statistically independent and illustrate its good properties with computer simulations.

0 citations0 reviewsNo code linkedOpen access