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.
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.
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.
In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its derivatives as a "non-smooth + non-smooth" optimization problem. Modern technique…
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.
Several techniques for domain adaptation have been proposed to account for differences in the distribution of the data used for training and testing. The majority of this work focuses on a binary domain label. Similar problems occur in a scientific context where there may be a continuous family of plausible data genera…
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.
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.
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.
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.
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).
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.
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.
In many real-world scenarios, an autonomous agent often encounters various tasks within a single complex environment. We propose to build a graph abstraction over the environment structure to accelerate the learning of these tasks. Here, nodes are important points of interest (pivotal states) and edges represent feasib…
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.
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.
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.
A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories, and in this case the vector spaces agree with the state spaces of the correspondi…
We study unsupervised multilingual alignment, the problem of finding word-to-word translations between multiple languages without using any parallel data. One popular strategy is to reduce multilingual alignment to the much simplified bilingual setting, by picking one of the input languages as the pivot language that w…
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.
We develop a pivotal test to assess the statistical significance of the feature variables in a single-layer feedforward neural network regression model. We propose a gradient-based test statistic and study its asymptotics using nonparametric techniques. Under technical conditions, the limiting distribution is given by …
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.
Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent topological features that can be used for any supervised or unsupervised learning…
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.
Paper simplifies data carving inference with a parametric distribution.
problem Valid inference after selection with data carving.
method Developed a parametric distribution for data carving inference.
result Exact inference for data carving can be computed trivially.
New DR method uses Gromov-Wasserstein distance for high-dimensional data.
problem Analyzing relationships between high-dimensional objects.
method Optimal transportation theory and Gromov-Wasserstein distance.
result Robust and efficient solution for complex high-dimensional datasets.
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.
Structural correspondence learning (SCL) is an effective method for cross-lingual sentiment classification. This approach uses unlabeled documents along with a word translation oracle to automatically induce task specific, cross-lingual correspondences. It transfers knowledge through identifying important features, i.e…
New method corrects missing data bias in dimension reduction.
problem Missing data complicates high-dimensional data analysis.
method Developed a bias-corrected Gram matrix for heterogeneous missingness.
result Proposed method improves dimension reduction techniques significantly.
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.
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…
Paper presents a new method for better financial market forecasting.
problem Traditional investment strategies fail to capture market nuances and risks.
method Combines deep learning, factor integration, and correlated stock analysis.
result Enhanced diversification and performance capture in financial markets.
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.
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of persistence diagrams is not Hilbert, they end up being difficult inputs for most Mach…
As much as data science is playing a pivotal role everywhere, healthcare also finds it prominent application. Breast Cancer is the top rated type of cancer amongst women; which took away 627,000 lives alone. This high mortality rate due to breast cancer does need attention, for early detection so that prevention can be…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their ability to represent uncertainty about predictions. In safety-critical applicatio…
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.
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…
FuBIF enhances AD by using real-valued functions for more flexible anomaly detection.
problem Limitations of the Isolation Forest in adaptability and bias.
method Introduces FuBIF, a generalization of IF using real-valued functions for branching in evaluation trees.
result FuBIF significantly improves flexibility and evaluation tree construction.
RPCholesky approximates kernel matrices with few evaluations.
problem Approximating kernel matrices efficiently.
method Randomly pivoted partial Cholesky factorization.
result RPCholesky provides nearly optimal low-rank approximations.
Paper presents LLM-enhanced contract metadata extraction.
problem Automatic detection and annotation of legal clauses in contracts.
method Integration of publicly available and proprietary datasets with advanced LLM methodologies.
result Substantial improvements in clause identification accuracy and efficiency.
FlowKac solves high-dimensional Fokker-Planck equations efficiently.
problem Intractability of Fokker-Planck equation solutions in high dimensions.
method Reformulates Fokker-Planck using Feynman-Kac, adaptive stochastic sampling, and normalizing flows.
result Significant computational efficiency and accuracy improvements over existing methods.
IDS improves RLHF by smoothing reward data, enhancing model performance.
problem Reward model performance degrades and overoptimization hinders true objective.
method Iterative Data Smoothing (IDS) updates model and data labels during each epoch.
result IDS outperforms traditional methods in RLHF.
Spectral method for joint community detection and group synchronization.
problem Jointly detecting communities and synchronizing orthogonal groups in graphs.
method Spectral decomposition followed by CPQR factorization.
result Near-optimal guarantees for exact and stable recovery of cluster memberships and orthogonal transforms.
MTRGL learns temporal correlations from multi-modal data for improved pair trading.
problem Discerning temporal correlations among financial entities.
method Combines time series data and discrete features into a temporal graph, using a memory-based temporal graph neural network.
result MTRGL outperforms traditional methods in temporal graph link prediction and pair trading.