Improved SVD for shifted matrices without explicit matrix construction.
problem Efficiently estimating SVD of shifted matrices.
method Shifted Randomized SVD algorithm.
result More efficient matrix factorization and low-rank approximation.
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48 results for “Shifted matrices”
We describe new results and algorithms for two different, but related, problems which deal with circulant matrices: learning shift-invariant components from training data and calculating the shift (or alignment) between two given signals. In the first instance, we deal with the shift-invariant dictionary learning probl…
We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special structure superimposed due to the time-shift. We demonstrate that the associated eigen…
GOPSA optimizes EEG data for cross-site age prediction, improving performance on multiple metrics.
problem Predictive shifts in EEG data from different sites and participants.
method Geodesic Optimization for Predictive Shift Adaptation (GOPSA) on the SPD manifold.
result Significantly higher performance on age prediction metrics compared to state-of-the-art methods.
New centrality-based graph shift operators improve graph neural networks.
problem Improving graph neural networks by enhancing graph shift operators.
method Proposed Centrality Graph Shift Operators (CGSOs) using global centrality metrics.
result CGSOs lead to improved performance in graph neural networks on real-world datasets.
A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting decomposed component scale matrices leads to a family of parsimonious models. An…
New method detects structural shifts in multivariate Hawkes processes.
problem Detecting changes in multivariate Hawkes processes.
method Using Fréchet statistics on overlapping windows of causal network.
result Accurately detects and characterizes changes in causal structure.
Faced with distribution shift between training and test set, we wish to detect and quantify the shift, and to correct our classifiers without test set labels. Motivated by medical diagnosis, where diseases (targets) cause symptoms (observations), we focus on label shift, where the label marginal changes but the …
This paper introduces a novel clustering algorithm for heteroscedastic Gaussian data without needing to know the number of clusters.
problem Clustering heteroscedastic Gaussian data without prior knowledge of the number of clusters.
method Introduces a novel cost function and fixed-point analysis to estimate centroids, introduces Wald kernel for measurement plausibility, and derives CENTRE-X algorithm.
result CENTRE-X algorithm can estimate centroids without prior knowledge of the number of clusters and performs comparably to standard algorithms K-means and Mean-Shift.
Study tackles distribution shift in combinatorial settings using matrix completion techniques.
problem Tackling distribution shift in combinatorial settings with rigorous statistical guarantees.
method Develops novel algorithms and theoretical results for extrapolating to test distributions not covered in training.
result Achieves bilinear combinatorial extrapolation under gradual spectral decay in high-dimensional data.
SCL discovers compositional structures in analogical reasoning tasks.
problem Discovering compositional structures in analogical reasoning tasks like Raven's Progressive Matrices.
method Proposes Scattering Compositional Learner (SCL) that composes neural networks in sequence.
result Achieves state-of-the-art performance on RPM datasets with significant improvements.
The low displacement rank (LDR) framework for structured matrices represents a matrix through two displacement operators and a low-rank residual. Existing use of LDR matrices in deep learning has applied fixed displacement operators encoding forms of shift invariance akin to convolutions. We introduce a class of LDR ma…
The paper analyzes Nordic stock markets' correlation structures and regime shifts.
problem Understanding and exploiting regime shifts in Nordic stock markets.
method Examined two decades of daily data for OMXS30, OMXC20, and OMXH25 universes; proposed an adaptive portfolio allocation framework.
result Documented pronounced regime dependence in rolling correlation matrices; proposed an adaptive portfolio allocation framework.
Meta learns low-rank covariance factors for better uncertainty estimation.
problem Sub-optimal covariance matrices in multi-task settings.
method Meta learns diagonal or diagonal plus low-rank factors using an attentive set encoder.
result Efficiently constructed task-specific covariance matrices improve uncertainty estimation.
Given a TQFT in dimension d+1, and an infinite cyclic covering of a closed (d+1)-dimensional manifold M, we define an invariant taking values in a strong shift equivalence class of matrices. The notion of strong shift equivalence originated in R. Williams' work in symbolic dynamics. The Turaev-Viro module associated to…
Unified view of label shift estimation methods.
problem Label distribution changes but class-conditional distributions remain the same.
method Unified view of two approaches: BBSE and MLLS.
result Unified framework and theoretical characterization of MLLS.
The Clifford group for 2 qubits is divided into 20 orbits, each with 4608 matrices.
problem Understanding the structure of the Clifford group for 2 qubits.
method Equivalence relation based on local Clifford gates and analysis of orbits.
result The Clifford group for 2 qubits is divided into 20 orbits, each with 4608 matrices.
Proposes a new divergence measure for probability distributions.
problem Challenges in estimating divergences from empirical samples.
method Embeds data into RKHS, computes Jensen-Shannon divergence between covariance operators.
result Establishes RJSD as a lower bound on Jensen-Shannon divergence, enabling variational estimation.
Optimal Algorithms in Linear Regression under Covariate Shift: On the Importance of Preconditionstat.ML
The paper explores optimal algorithms for linear regression under covariate shift, proving the optimality of certain transformations and SGD variants.
problem Optimal algorithms for linear regression under covariate shift with ellipse-shaped constraints.
method Establishes a tight lower generalization bound via Bayesian Cramer-Rao inequality, proves the optimality of certain transformations, and analyzes SGD variants.
result Optimal estimators and SGD variants achieve optimality under specific conditions.
Enhances UPSA to reduce noise in financial data.
problem Noise in financial data affects UPSA's performance.
method Time-averaging optimal penalty weights and using Average Oracle correlation eigenvalues.
result Combining time-averaging and Average Oracle correlation eigenvalues improves UPSA's performance.
Spectral portfolio theory links neural networks to wealth dynamics via SGD weight matrices.
problem Understanding wealth dynamics from neural network training.
method Direct identification of weight matrices as portfolio allocation matrices, linking SGD forces to portfolio dynamics.
result Spectral properties of SGD weight matrices transition between additive and multiplicative regimes, influencing wealth dynamics.
Novel parametrized graph shift operators improve graph neural network performance.
problem Improving graph neural network performance on various datasets.
method Proposed a novel parametrized graph shift operator (PGSO) that optimizes parameters during training.
result PGSO improves accuracy in node and graph classification tasks on real-world datasets.
We propose a simple method to learn linear causal cyclic models in the presence of latent variables. The method relies on equilibrium data of the model recorded under a specific kind of interventions ("shift interventions"). The location and strength of these interventions do not have to be known and can be estimated f…
The paper analyzes how combining samples from two tasks can improve performance, especially in high dimensions.
problem Understanding when combining samples from two related tasks outperforms learning with one task alone.
method Applying random matrix theory to high-dimensional linear regression, focusing on proportional sample size increases.
result Precise high-dimensional asymptotics for bias and variance of HPS estimator, showing phase transitions in transfer performance.
Study reveals an equivalence principle for the spectrum of random inner-product kernel matrices in polynomial scaling.
problem Understanding the spectrum of random kernel matrices in polynomial scaling regimes.
method Investigates random matrices with nonlinear kernel functions applied to inner products of uniformly distributed vectors.
result The spectrum of the random kernel matrix is asymptotically equivalent to a simpler matrix model through free additive convolution.
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix with , by a partial circulant matrix with rows related by circular shifts. Partial circulant matrices admit fast implementations via Fourier tra…
Paper introduces OMD for ordered state transitions in SSMs.
problem Modeling ordered latent states in dynamic systems.
method Ordered Matrix Dirichlet (OMD) prior over ordered stochastic matrices.
result OMD models recover interpretable ordered latent structure without sacrificing predictive performance.
Out-of-Distribution Generalization of In-Context Learning: A Low-Dimensional Subspace Perspectivestat.ML
Paper provides a mathematical model for transformer ICL out-of-distribution generalization.
problem Understanding when transformer in-context learning can generalize beyond pre-training data.
method Minimal mathematical model of linear regression tasks with low-rank covariance matrices, analyzing distribution shifts as varying angles between subspaces.
result Transformers can generalize to all angle shifts if pre-training tasks are drawn from a union of subspaces, but not from a single Gaussian.
The study examines denoising and noisy-input regression under distribution shift, revealing double descent behavior and insights for data augmentation.
problem Understanding denoising in machine learning, especially under noisy inputs and distribution shift.
method Theoretical analysis of supervised denoising and noisy-input regression, considering low-rank data and proportional regime.
result The test error exhibits double descent under general distribution shift, indicating that overfitting the noise can be benign, tempered, or catastrophic.
New method for identifying graph shift operators using vertex-time autoregressive models.
problem Identifying graph shift operators from graph signals.
method Online optimization using vertex-time autoregressive model and stochastic gradient projection.
result Successful recovery of graph shift operators from graph signals.
We study the sample complexity of canonical correlation analysis (CCA), \ie, the number of samples needed to estimate the population canonical correlation and directions up to arbitrarily small error. With mild assumptions on the data distribution, we show that in order to achieve -suboptimality in a properly define…
Proposes CAL to learn causal adjacency for better spatiotemporal prediction.
problem Suboptimal performance in spatiotemporal prediction due to out-of-distribution data.
method Causal Adjacency Learning (CAL) method to discover causal relations over graphs.
result Calculated causal adjacency matrix enhances prediction performance on out-of-distribution test data.
Hybrid ResNet and RMT improve covariance matrix estimation for cryptocurrency portfolios.
problem Noisy, non-Gaussian financial data leads to unstable covariance matrices.
method Combines RMT regularization and ResNet learning for data-driven corrections.
result Hybrid estimator outperforms traditional methods in portfolio optimization.
Improved market state classification for risk assessment.
problem Classifying financial market states for better risk assessment.
method Modified selection criteria for market states, clustering optimization, and visualization of correlation matrices.
result Statistically significant results in SP 500 and Nikkei 225 markets.
Hessian alignment improves OOD generalization in deep learning.
problem Improving deep learning models' ability to generalize to out-of-distribution data.
method Analyzed Hessian and gradient alignment for domain generalization using recent OOD theory.
result Hessian alignment methods achieve promising performance on various OOD benchmarks.
Tensor methods have emerged as a powerful paradigm for consistent learning of many latent variable models such as topic models, independent component analysis and dictionary learning. Model parameters are estimated via CP decomposition of the observed higher order input moments. However, in many domains, additional inv…
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtu…
Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least squares regression, canonical-correlation analysis and Fisher discriminant analysis. R…
Study on unknotting twisted knots using arc shift and region arc shift moves.
problem Unknotting twisted knots and finding bounds for region arc shift number.
method Introduced arc shift move and region arc shift move for twisted knots.
result Found families of twisted knots with specific arc shift and region arc shift numbers.
Study detects concept shift in online data using martingales.
problem Detecting concept shift in online datasets.
method Exchangeable martingales and conformal prediction techniques.
result Decomposes concept shift into detectable components.
Geometrically Interpreting Higher Cup Products, and Application to Combinatorial Pin Structureshep-th
Geometrically interprets cup products and defines combinatorial Pin structures.
problem Understanding Steenrod's cup products and their geometric interpretation.
method Constructs vector fields and combinatorial frames to interpret cochain-level formulas.
result Geometrically interprets cup products and defines Pin structures combinatorially.
Paper proposes SJS model to estimate model performance under covariate and label shifts.
problem Estimating model performance when both covariates and labels shift.
method Sparse Joint Shift (SJS) model and SEES algorithm.
result SEES achieves significant shift estimation error improvements over existing approaches.
Extends FJS analysis to general label spaces, including classification and regression.
problem Distribution shift in general label spaces, including covariate and label shifts.
method Proposes a framework for analyzing FJS in general label spaces and generalizes existing results.
result Generalizes FJS analysis to general label spaces, including classification and regression.
A method to explain disease transformation using biomarker covariance matrices.
problem Understanding disease transformation from a healthy baseline.
method Modeling healthy and disease states of biomarker covariance matrices to characterize perturbations.
result Disease perturbs the biomarker covariance structure, allowing for mechanistic explanations and individual patient prognosis.
Paper tackles high-dimensional quantile regression with distribution shift using transfer learning.
problem Efficiency of knowledge transfer is severely impacted by distribution shift in high-dimensional regression.
method Proposes a novel transferable set and framework for three types of distribution shift: parameter, covariate, and residual.
result Establishes estimation error bounds and source detection consistency for the proposed method.
Unified learning bound for covariate and concept shifts.
problem Generalization under distribution shift in machine learning.
method Support-agnostic definitions of covariate and concept shifts using entropic optimal transport, leading to a unified error bound applicable to various loss functions and label spaces.
result Development of estimators for shifts with concentration guarantees and the DataShifts algorithm for quantifying and estimating the error bound.
Proposes SGShift to identify shifted features causing model performance degradation under concept shift.
problem Concept shift leading to miscalibration in ML models across domains.
method SGShift method for identifying sparse set of shifted features using feature selection and statistical tools.
result SGShift identifies shifted features more accurately than baseline methods, requires few samples in the shifted domain, and is robust to complex cases.
New contact structures defined on differentiable stacks.
problem Defining contact structures on differentiable stacks.
method Introducing -shifted and -shifted contact structures.
result Shifted contact structures provide new insights into geometry.