Two Kähler structures are PCR equivalent in the Siegel domain.
problem Equivalence of two Kähler structures in the Siegel domain.
method Construction of complex hyperbolic and Kähler structures from Sasakian structure.
result PCR Kähler equivalent structures in Siegel domain.
Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy, missing, and mixed-valued, i.e., discrete and continuous, covariates is not understoo…
PCR-LE achieves optimal rates for nonparametric regression over Sobolev spaces.
problem Nonparametric regression over Sobolev spaces with random design.
method PCR-LE using Laplacian Eigenmaps on neighborhood graphs.
result PCR-LE achieves minimax rates of convergence for both estimation and goodness-of-fit testing.
CPCR mitigates bias in PCR for overparameterized models.
problem Bias in Principal Component Regression (PCR) for overparameterized models.
method Calibrated Principal Component Regression (CPCR) learns a low-variance prior in the PC subspace and calibrates the model in the original feature space.
result CPCR outperforms standard PCR in overparameterized settings, improving prediction across multiple problems.
VC-PCR improves prediction by clustering correlated variables.
problem Decreased prediction accuracy due to cluster structure in predictor variables.
method Supervised variable selection and clustering to integrate cluster information into a sparse modeling process.
result VC-PCR achieves better prediction, variable selection, and clustering performance.
New approach to quantify posterior concentration rates using Wasserstein dynamics.
problem Quantifying the speed of posterior distribution concentration in Bayesian statistics.
method Combining local Lipschitz-continuity with dynamic formulation of Wasserstein distance.
result Optimal posterior contraction rates in finite and infinite-dimensional models.
Noisy Pooled PCR tests large groups more efficiently.
problem Efficiently test large populations for viral infections.
method Converts group testing to a linear inverse problem with a message passing algorithm.
result Estimates patient illness status with fewer pooled measurements.
This study analyzes prediction risk for PCR method in latent factor regression models.
problem Prediction risk analysis in latent factor regression models.
method Adaptive PCR method with risk bounds established under factor regression model.
result Unified framework for analyzing various linear prediction methods under factor regression.
Deep learning accelerators efficiently train over vast and growing amounts of data, placing a newfound burden on commodity networks and storage devices. A common approach to conserve bandwidth involves resizing or compressing data prior to training. We introduce Progressive Compressed Records (PCRs), a data format that…
Improved fMRI analysis models enhance classification performance and select relevant brain regions.
problem Inaccurate selection of relevant brain components in MVPA models.
method Hybrid Sparsity-Ranked LASSO (JSRL) method integrating component-level and voxel-level activity.
result JSRL models achieve up to 51.7% improvement in cross-validated deviance R2 and 7.3% improvement in cross-validated AUC. Principal Components Regression (PCR) is a traditional tool for dimension reduction in linear regression that has been both criticized and defended. One concern about PCR is that obtaining the leading principal components tends to be computationally demanding for large data sets. While random projections do not possess…
Adaptive PCR improves panel data analysis with uniform guarantees.
problem Adaptive data collection in panel data settings.
method Adapting PCR to online settings using martingale concentration.
result Time-uniform guarantees for adaptive PCR in panel data.
A new PCR method using SVD with sparse regularization.
problem Lack of response variable information in traditional PCR.
method One-stage SVD approach with two loss functions and sparse regularization.
result Obtains principal component loadings with response variable information.
We solve principal component regression (PCR), up to a multiplicative accuracy 1+γ, by reducing the problem to O~(γ−1) black-box calls of ridge regression. Therefore, our algorithm does not require any explicit construction of the top principal components, and is suitable for large-scale PCR instances. In…
New method infers viral load from pooled tests.
problem Inefficient viral load inference in pooled testing.
method Message passing algorithm with PCR noise function.
result Accurate viral load inference possible.
We identify and validate a model for PCR in high dimensions, improving prediction guarantees.
problem Model identification and out-of-sample prediction in high-dimensional error-in-variables settings.
method Analysis of principal component regression (PCR) in fixed design settings, introducing a linear algebraic condition.
result Consistent model identification and improved out-of-sample prediction guarantees.
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…
Consider a regression problem where there is no labeled data and the only observations are the predictions fi(xj) of m experts fi over many samples xj. With no knowledge on the accuracy of the experts, is it still possible to accurately estimate the unknown responses yj? Can one still detect the leas…
Technological change and innovation are vitally important, especially for high-tech companies. However, factors influencing their future research and development (R&D) trends are both complicated and various, leading it a quite difficult task to make technology tracing for high-tech companies. To this end, in this pape…
A new debiasing method for high-dimensional regression with applications to PCR.
problem Debiasing in high-dimensional statistics with i.i.d. samples and sub-Gaussian covariates.
method Spectrum-Aware Debiasing using rescaled gradient descent with spectral information.
result Achieves debiasing in broader contexts with structured dependencies, heavy tails, and low-rank structures.
New method speeds up learning of complex dynamical systems.
problem Efficiently learning large-scale dynamical systems from finite data.
method Random projections (sketching) to boost kernel-based Koopman operator estimators.
result The proposed estimators maintain accuracy while significantly reducing computation time.
This paper investigates the efficacy of a regularized multi-task learning (MTL) framework based on SVM (M-SVM) to answer whether MTL always provides reliable results and how MTL outperforms independent learning. We first find that M-SVM is Bayes risk consistent in the limit of large sample size. This implies that despi…
Machine learning predicts ship performance changes over time.
problem Estimating ship hydrodynamic performance over time.
method Machine learning methods (NL-PCR, NL-PLSR, probabilistic ANN) calibrated with in-service data.
result Probabilistic ANN model performs best in predicting ship performance changes.
Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components a…
Machine learning model diagnoses COVID-19 from routine blood tests.
problem Difficulty in diagnosing COVID-19 due to inconsistent blood parameter changes.
method Constructed a machine learning model using 5,333 patients with various infections and 160 COVID-19-positive patients.
result Cross-validated AUC of 0.97, sensitivity of 81.9%, specificity of 97.9%.
A new method improves target selection for manipulating complex systems like the brain.
problem Improper incorporation of low-variance outcomes into latent space of predictive models.
method Developed a novel objective based on supervised variational autoencoders (SVAEs) for PPCA (Probabilistic Principal Component Analysis).
result gPCR (Generative Principal Component Regression) dramatically improves target selection in manipulation compared to standard PCR and SVAEs.
We analyze optimal weighted ridge regression in overparameterized linear models.
problem Optimal regularization in overparameterized linear regression models.
method Generalized ridge regression with weighted regularization.
result The optimal regularization parameter can be negative in overparameterized settings.
Predicting response to neoadjuvant therapy is a vexing challenge in breast cancer. In this study, we evaluate the ability of deep learning to predict response to HER2-targeted neo-adjuvant chemotherapy (NAC) from pre-treatment dynamic contrast-enhanced (DCE) MRI acquired prior to treatment. In a retrospective study enc…
Bayesian nonparametric models get better posterior estimates via SPDE methods.
problem Estimating posterior distributions in nonparametric Bayesian models.
method Extending diffusion methods to SPDEs on Hilbert spaces for posterior contraction and Laplace approximation.
result Derivation of posterior contraction rates and finite-sample Bernstein von Mises results.
PLS-Lasso integrates dimension reduction into regression for financial index tracking.
problem Dimension reduction and regression are traditionally treated separately in multivariate data analysis.
method PLS-Lasso integrates dimension reduction directly into the regression process, presenting two formulations: PLS-Lasso-v1 and PLS-Lasso-v2.
result PLS-Lasso-v1 and PLS-Lasso-v2 outperform Lasso in financial index tracking.
New method models aptamer libraries as Boltzmann-weighted graph ensembles for better affinity predictions.
problem Anomalous candidates in SELEX datasets obscure true aptamer-ligand affinity.
method Boltzmann graph ensemble embeddings for thermodynamically parameterized exponential-family random graphs.
result Proposed embedding enables robust community detection and subgraph-level explanations for aptamer ligand affinity.
Efficiently integrates stiff ODEs with vectorized methods.
problem Stiff systems and sparse training data in ODEs.
method Implicit, vectorized time integration with adjoint method.
result Achieves speed ups of greater than 100x on modern GPUs.
Software helps teach latent variable methods in multivariate data analytics.
problem Challenges in understanding multivariate data analytics for students.
method Interactive software for comparing latent variable methods.
result Builds intuition on choosing methods and interpreting coefficients.
Gradient-free ensemble learns sector forecasts from diverse models.
problem Predicting sector returns in a volatile market.
method Dynamic model combination using out-of-sample R-squared.
result Ensemble outperforms individual models in sector rotation.
Research proposes a risk-free machine learning model for COVID screening from routine blood tests.
problem Rapid antigen tests have low sensitivity and are not suitable for widespread screening.
method Stacked Ensemble Machine Learning model using routine blood tests.
result 100% accuracy, precision, recall and F1-score in identifying COVID patients.
Linear models can overfit without harming OOD generalization under certain conditions.
problem Understanding how overparameterized linear models generalize to out-of-distribution data.
method Analyzing overparameterized linear models under covariate shift, providing guarantees for OOD generalization.
result Benign overfitting occurs in standard ridge regression under OOD conditions, with specific structural conditions on target covariance.
New method detects RNA modifications without prior training, revealing novel sites.
problem Detecting RNA modifications with high accuracy and sensitivity.
method Anomaly detection using nanopore raw ionic current signals and nearest neighbor comparison.
result Detects diverse RNA modifications without prior training, including a novel 2'-O-methylated site in DENV.
Paper solves equivalence problems for fifth-order differential operators using Cartan's method.
problem Equivalence problem for fifth-order differential operators under fiber-preserving transformations.
method Cartan's method of equivalence applied to solve two versions of the equivalence problem.
result Sufficient and necessary conditions for fiber-preserving transformations between fifth-order differential operators.
In this paper we discuss four problems regarding Markov equivalences for subclasses of loopless mixed graphs. We classify these four problems as finding conditions for internal Markov equivalence, which is Markov equivalence within a subclass, for external Markov equivalence, which is Markov equivalence between subclas…
We consider equivalence relations among smooth map germs with respect to geometry of G-structures on the target space germ. These equivalence relations are natural generalization of right-left equivalence (i.e., A-equivalence) in the sense of Thom-Mather depending on geometric structures on the target space germ. Unfor…
We examine an equivalence relation between free homotopy classes of closed curves on the pair of pants known as k-equivalence, a generalization of a concept previously defined by Leininger. We prove that two classes of closed curves on the pair of pants that are k-equivalent must also be 1-equivalent and 2-equivalent. …
This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the equivalence problems: first via the direct equivalence problem, second equivalence pro…
Equivalent bicategories constructed from action Lie groupoids.
problem Equivalence of bicategories constructed from action Lie groupoids.
method Localizing at equivariant weak equivalences, surjective submersive equivariant weak equivalences, and all weak equivalences.
result Weak equivalences between action Lie groupoids are isomorphic to compositions of nice forms of equivariant weak equivalences.
In the context of finite type invariants, Stanford introduced a family of equivalence relations on knots defined by the lower central series of the pure braid groups and characterized the finite type invariants in terms of the structure of the braid groups. It is known that this equivalence and Ohyama's equivalence def…
Develops L∞ spaces over dg manifolds and establishes an equivalence with L∞ algebroids.
problem Defining and comparing L∞ spaces and algebroids over dg manifolds. method Establishes an equivalence between categories of L∞ algebroids and L∞ spaces, constructs a faithful functor. result Detects weak equivalences between L∞ algebroids and L∞ spaces. Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent when the sets of lengths of their (primitive) closed geodesics are equal. We give a general construction of eigenvalue equ…
Paper refines braidoid equivalence for spherical knotoids.
problem Equivalence of knotoid diagrams in spherical space.
method Refined L-equivalence of braidoid diagrams. result Equivalence theorem for multi-knotoid diagrams in S2. The ν+-equivalence is an equivalence relation on the knot concordance group. This relation can be seen as a certain stable equivalence on knot Floer complexes CFK∞, and many concordance invariants derived from Heegaard Floer theory are invariant under the equivalence. In this paper, we show that any genus …