Random walk speed on Teichmüller space is a proper function.
problem Understanding the speed of random walks on Teichmüller space.
method Adaptation of Gouëzel's pivoting techniques to Teichmüller space.
result Speed of random walk is a proper function on Teichmüller space.
Paper reinterprets ARP algorithm and improves its analysis and speed.
problem Column subset selection in data analysis.
method Volume sampling and active learning connections, new analysis, rejection sampling.
result Faster implementations and new analysis for ARP algorithm.
New pivoting strategy improves trace norm contraction in low-rank approximation.
problem Finding good low-rank approximations of symmetric, positive-definite matrices.
method Choosing rows with likelihood proportional to Aii2 for randomly pivoted partial Cholesky algorithm. result Same trace norm contraction result in Frobenius norm for improved pivoting strategy.
A comparison-based algorithm finds nearest neighbors in metric spaces.
problem Finding nearest neighbors without direct distance information.
method Recursive splitting using random pivot points to form a comparison tree.
result The height of the comparison tree is logarithmic in the number of points, leading to efficient search performance.
Exact selective inference with randomization for Gaussian regression models.
problem Exact selective inference in Gaussian regression models.
method Introduces a pivot for exact selective inference with randomization, reducing the problem to a bivariate truncated Gaussian distribution.
result Our pivot leads to exact inference and produces narrower confidence intervals than related methods.
New quadrature method using randomly pivoted Cholesky outperforms existing techniques.
problem Efficiently approximating integrals of functions in reproducing kernel Hilbert spaces.
method Nodes drawn by randomly pivoted Cholesky algorithm.
result Randomly pivoted Cholesky quadrature is fast and achieves comparable accuracy to more computationally intensive methods.
Develops an empirical likelihood framework for random forests and ensembles.
problem Quantifying the statistical uncertainty of random forests and ensembles.
method Empirical likelihood framework exploiting the incomplete U-statistic structure of ensemble predictions. result Modified empirical likelihood statistic achieves accurate coverage and practical reliability.
PiVoT improves real-time multi-object detection and tracking in clutter.
problem Challenges in multi-object detection and tracking from noisy point clouds.
method Variational inference for fast, clutter-resilient multi-object tracking.
result Substantial performance improvement over existing Bayesian trackers.
Methods for prediction and tolerance intervals in non-normal models.
problem Constructing prediction and tolerance intervals for non-normal data.
method Two approaches: pivotal quantity approximation and confidence interval for mean.
result Intuitive, simple, efficient methods with proper operating characteristics.
A graph abstraction speeds up reinforcement learning in complex environments.
problem Learning hierarchical reinforcement learning tasks in complex environments.
method Jointly trains a latent pivotal state model and a curiosity-driven policy. Uses a world graph to guide high-level and low-level agents.
result Significant performance and efficiency improvements over baseline methods.
Study random walks on groups with superlinear divergent geodesics.
problem Existence of superlinear divergent geodesics in groups.
method Developed theory of superlinear divergence and applied Gouëzel's pivoting technique.
result Established a central limit theorem for random walks on groups with superlinear divergent geodesics.
Deviation inequalities and limit laws for random walks on metric spaces.
problem Understanding random walks on metric spaces with contracting isometries.
method Adapting Gouëzel's pivotal time construction to establish deviation inequalities.
result Exponential bounds and limit laws for random walks on mapping class groups and CAT(0) spaces.
Study on knotting in very long polymer chains, finding Poisson distribution for prime knot types.
problem Understanding knotting in very long polymer chains.
method Generated and analyzed 243−k polygons of size n=2k using tree data structure and pivot algorithm. Used new knot diagram simplification and invariant-free classification. result Number of prime summands of knot type K in a random n-gon is well described by a Poisson distribution. Adapts pivoting technique to circle homeomorphisms for proofs.
problem Probabilistic Tits alternative and exponential synchronization.
method Adapts Gou{ë}zel's pivoting technique.
result Different proofs of probabilistic Tits alternative and exponential synchronization.
Optimization can learn Johnson-Lindenstrauss embeddings without randomization.
problem Achieving compact data representations with theoretical guarantees.
method A novel optimization-based approach over the space of random solution samplers.
result The method avoids bad stationary points and converges to a deterministic solution.
String-net models explore non-spherical fusion categories, revealing new spin structures and representations.
problem Investigating string-net models in non-spherical fusion categories.
method String-net models associate vector spaces to surfaces in terms of graphs decorated by objects and morphisms of a pivotal fusion category.
result String-net spaces count r-spin structures and carry representations of the mapping class group.
This paper analyzes Local SGD for federated learning, achieving both statistical and communication efficiency.
problem Statistical estimation and inference in federated learning with decentralized data.
method Local SGD, a multi-round estimation procedure using intermittent communication.
result Local SGD achieves both statistical efficiency and communication efficiency.
The study analyzes convergence rates for sparse pivotal estimators in high-dimensional regression.
problem Sparse pivotal estimation in high-dimensional regression problems.
method Theoretical analysis and comparison of non-smooth + non-smooth optimization problems, including smoothing techniques.
result Minimax sup-norm convergence rates for square-root Lasso-type estimators are derived.
Estimates proportions of LLM-generated text in mixed documents.
problem Estimating the proportion of text generated by a pre-specified LLM in mixed documents.
method Developed estimators for two observation regimes: full observation and pivotal reduction, and established sample complexity bounds.
result Full observation estimators require fewer samples than pivotal reduction estimators.
Develops graphical calculus for monoidal categories with twisted pivotal structures.
problem Constructing modules for surfaces with Morse functions or foliations.
method Graphical calculus and string nets for monoidal categories with twisted pivotal structures.
result Twisted string net modules assemble in an oriented categorified 2-TQFT.
Adversarial networks enforce pivotal property for robust inference.
problem Continuous family of data generation processes in scientific contexts.
method Adversarial networks to enforce pivotal property.
result Demonstrated effectiveness in a toy example and particle physics.
Study on estimating Gumbel--Max watermark proportions in edited documents.
problem Estimating the proportion of a document generated from a watermarked LLM.
method Comparison of full observation and pivotal reduction observation regimes; development of estimators and information-theoretic lower bounds.
result Full observation yields a substantially smaller sample complexity compared to pivotal reduction.
New construction of Turaev-Viro invariants invariant under Morita equivalence.
problem Constructing Turaev-Viro invariants invariant under Morita equivalence.
method Pivotal bicategory construction of spherical module categories.
result The invariant recovers the standard Turaev-Viro invariant and is independent of the skeleton.
New algorithm improves plant breeding by clustering soybean genotypes more accurately and efficiently.
problem Low accuracy and high computational complexity in clustering plant genotypes.
method Spectral Clustering with Pivotal Sampling for phenotypic data.
result Our algorithm achieves substantially more accuracy than existing methods.
We extend the notion of an ambidextrous trace on an ideal (developed by the first two authors) to the setting of a pivotal category. We show that under some conditions, these traces lead to invariants of colored spherical graphs (and so to modified 6j-symbols).
Proposes using Wasserstein barycenter for better multilingual alignment.
problem Finding word-to-word translations between multiple languages without parallel data.
method Uses Wasserstein barycenter as a more informative pivot language, minimizing pairwise transportation costs.
result Demonstrates state-of-the-art performances on standard benchmarks.
New method for online inference using SGD with random scaling.
problem Efficient online inference for SGD parameters.
method Asymptotic pivotal statistics via random scaling.
result Robust and efficient online inference without resampling.
Generalizes string-net modular functors to non-spherical categories.
problem Extending string-net models to non-spherical categories.
method Using non-semisimple string-nets and Drinfeld centers.
result Equivalence between string-net and Lyubashenko modular functors.
Completely random measures (CRM) represent the key building block of a wide variety of popular stochastic models and play a pivotal role in modern Bayesian Nonparametrics. A popular representation of CRMs as a random series with decreasing jumps is due to Ferguson and Klass (1972). This can immediately be turned into a…
This article provides a new toolbox to derive sparse recovery guarantees from small deviations on extreme singular values or extreme eigenvalues obtained in Random Matrix Theory. This work is based on Restricted Isometry Constants (RICs) which are a pivotal notion in Compressed Sensing and High-Dimensional Statistics a…
Estimates watermarked content proportions in mixed-source texts.
problem Optimally estimating the proportion of watermarked content in texts with mixed sources.
method Casting the problem as estimating a proportion parameter in a mixture model based on pivotal statistics.
result Proposes efficient estimators for watermark proportion and shows their accuracy through evaluations.
The paper analyzes how much data points can be altered to change their rank in nearest neighbor searches.
problem Vulnerability of nearest neighbor search in high-dimensional data.
method Statistical analysis of perturbation needed to change neighbor rank.
result Derived statistical distribution of perturbation needed to modify neighbor rank.
A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the…
Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness, achieving linear convergence. However, these methods are either based on computations o…
New 4-manifold invariant defined from trisection diagrams.
problem Defining a new 4-manifold invariant from trisection diagrams.
method Algebraic data from bimodule categories and spherical fusion categories, described diagrammatically.
result Includes Hopf algebraic invariants and modular fusion category invariants.
Abstract: Cyber-security challenges tackled with machine learning.
problem Cyber-security problems and lack of labeled data.
method Provided novel data sets and a method to generate labels via pivoting.
result Solutions for generating labels in cyber-security.
PIVOT bridges Black-Scholes price and implied volatility spaces via a differentiable layer.
problem Lack of a differentiable interface between price and implied volatility spaces.
method Develops PIVOT, a differentiable layer that preserves LBR's forward pass and avoids backpropagation through branch logic, addressing singularity issues.
result PIVOT achieves high performance and accuracy, reducing price and implied volatility errors by up to 43.4% and 21.3% respectively.
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The method is based on linear programming only, so that its numerical implementation is…
Accelerated RPCholesky speeds up kernel matrix approximations.
problem Efficiently approximating large kernel matrices.
method Accelerated randomly pivoted Cholesky (RPCholesky) with block matrix computations and rejection sampling.
result Approximates kernel matrices up to 40 times faster.
MOSAIC detects change points in dynamic networks with low-rank and sparse changes.
problem Detecting change points in dynamic networks with specific structural properties.
method Eigen-decomposition-based test with screened signals and residual-based adjustment.
result MOSAIC achieves minimax-optimal detection and testing rates.
Novel framework uses synthetic data to quantify uncertainty in complex data.
problem Uncertainty quantification in complex, unstructured data.
method Perturbation-Assisted Sample Synthesis (PASS) and Perturbation-Assisted Inference (PAI) framework.
result Statistically guaranteed validity in inference, enhancing reliability of synthetic data.
New method improves BO's AF maximizer initialization for high-dimensional problems.
problem Challenges in maximizing acquisition functions in high-dimensional Bayesian optimization.
method Proposes a heuristic optimizer-based initialization approach to improve AF maximizer performance.
result Our approach significantly enhances BO performance in most test cases.
New algorithm detects changes in high-dimensional data with mean and variance.
problem Challenges in detecting changes in high-dimensional data with mean and variance.
method Complete graph-based approach to detect changes of mean and variance from low to high-dimensional online data.
result The proposed method outperforms existing methods in terms of detection power.
Paper proposes a method for cross-lingual sentiment classification using distributed word representations.
problem Cross-lingual sentiment classification with strict one-to-one word mapping limitations.
method Uses distributed word representations to learn meaningful one-to-many mappings for pivot words.
result Method outperforms state-of-the-art in cross-lingual sentiment classification.
The paper constructs semistrict monoidal 2-categories from foam evaluations.
problem Creating examples of semistrict monoidal 2-categories.
method Using a closed foam evaluation formula as input, the paper rigorously constructs semistrict monoidal 2-categories.
result The constructed monoidal 2-categories are semistrict, have duals and adjoints, and carry a spatial duality structure.
PANDA improves linear discriminant analysis in high dimensions with minimal tuning.
problem Linear discriminant analysis in high-dimensional settings.
method PANDA: a tuning-insensitive method for linear discriminant analysis.
result PANDA achieves optimal convergence rates in estimation error and misclassification rate.
Parallel training speeds up neural network training, but process communication costs limit efficiency.
problem Efficiently training complex neural networks in real-time.
method Implemented Network Parallel Training using Cannon's Algorithm for matrix multiplication.
result Increasing the number of processes speeds up training until communication costs become prohibitive.
Data mining techniques predict breast cancer types with high accuracy.
problem Early detection of breast cancer to reduce mortality rates.
method Twelve classification algorithms applied to the Breast Cancer Wisconsin dataset.
result High accuracy in predicting malignant and benign breast cancer.