Open manifolds with nonnegative Ricci curvature have virtually abelian fundamental groups if they escape from bounded balls at a small rate.
problem Understanding the fundamental groups of open manifolds with nonnegative Ricci curvature.
method Analyzing the escape rate of minimal geodesic loops and relating it to the fundamental group's properties.
result If an open manifold has a small escape rate, its fundamental group is virtually abelian.
New method for evaluating LLMs reduces bias in open-ended evaluations.
problem Bias in Elo-based ratings of LLMs due to data redundancies.
method Proposes evaluation as a 3-player game and introduces novel solution concepts.
result Novel method leads to more robust and intuitive ratings.
Study optimal rates for multiclass classification, resolving open questions.
problem Optimal rates for multiclass classification with any label space.
method Establishes optimal rates for all hypothesis classes, defining new tree structures.
result Optimal rates for multiclass classification with no infinite DSL trees.
Analyzes Indian commercial dynamism using time series data.
problem Understanding commercial dynamism in India.
method Time series analysis of various economic indicators.
result Detailed insights into growth rate, trade balance, etc.
An RNN-Survival model predicts optimal email send times based on recipient behavior.
problem Predicting optimal send times for emails to maximize open rates.
method Recurrent Neural Network (RNN) in a survival model framework.
result The RNN-Survival model outperforms traditional survival analysis in predicting times-to-open.
A consequence of the Cheeger-Gromoll splitting theorem states that for any open manifold (M,x) of nonnegative Ricci curvature, if all the minimal geodesic loops at x that represent elements of π1(M,x) are contained in a bounded ball, then π1(M,x) is virtually abelian. We generalize the above result: if these …
Stability proved for open Milne spacetime, showing gravity's long-term behavior.
problem Global stability of open Milne spacetime for Einstein-scalar field equations.
method Gaussian normal coordinates, exploiting expanding geometry of Milne spacetime.
result Spatial metric tends to hyperbolic metric as time goes to infinity.
Open AI models affect bond yields differently than closed ones.
problem Understanding how market reactions to AI releases impact bond yields.
method Analyzed US bond yields before and after the release of open and closed AI models.
result Open AI models shift bond yields in the opposite direction of closed models.
Open category detection is the problem of detecting "alien" test instances that belong to categories or classes that were not present in the training data. In many applications, reliably detecting such aliens is central to ensuring the safety and accuracy of test set predictions. Unfortunately, there are no algorithms …
We explicitly test if the reliability of credit ratings depends on the total number of admissible states. We analyse open access credit rating data and show that the effect of the number of states in the dynamical properties of ratings change with time, thus giving supportive evidence that the ideal number of admissibl…
We study streaming principal component analysis (PCA), that is to find, in O(dk) space, the top k eigenvectors of a d×d hidden matrix Σ with online vectors drawn from covariance matrix Σ. We provide global convergence for Oja's algorithm which is popularly used in practice but lacks t…
Predicting discomfort glare in open-plan offices is a challenging problem. Although glare research has existed for more than 50 years, all current glare metrics have accuracy limitations, especially in open-plan offices with low lighting levels. Thus, it is crucial to develop a new method to predict glare more accurate…
Study finds discrepancies in open interest reporting for Bitcoin perpetual swaps.
problem Misquoted open interest in perpetual swaps leads to liquidity and solvency concerns.
method Analyzed tick-by-tick data from seven exchanges to identify discrepancies.
result Open interest reported by exchanges varies widely, some implausible.
D-Adaptation automatically sets optimal learning rates without manual tuning.
problem Optimizing learning rates for efficient convergence in machine learning.
method D-Adaptation, which asymptotically achieves optimal learning rates without back-tracking or additional evaluations.
result D-Adaptation automatically matches hand-tuned learning rates across diverse problems.
Proposes a more robust rating scale for banks.
problem Inconsistent rating scale validation leading to higher capital requirements.
method Develops a new rating scale that is statistically distinguishable and robust.
result Reduces the calibration probability of default, saving capital requirements.
New algorithms achieve uniform stability for empirical risk minimization.
problem Designing uniformly stable optimization algorithms for empirical risk minimization.
method Black-box conversion of smooth optimization algorithms and development of Mirror Descent for smooth optimization.
result Optimal algorithms with uniform stability and convergence rates for smooth optimization.
We present a large scale data set, OpenEDS: Open Eye Dataset, of eye-images captured using a virtual-reality (VR) head mounted display mounted with two synchronized eyefacing cameras at a frame rate of 200 Hz under controlled illumination. This dataset is compiled from video capture of the eye-region collected from 152…
New approach uses 'growth' and 'harvesting' concepts to improve deep learning models.
problem Current deep learning models lack transparency and high convergence rates.
method Reconsider neural networks as single-species population dynamics with balanced growth and harvesting rates.
result SGD with balanced growth and harvesting rates outperforms adaptive methods in all three requirements.
Proposes a new framework for discount models.
problem Arbitrage-free dynamic framework for discount models.
method Derives general consistency conditions for factor models.
result Alternative to Heath--Jarrow--Morton framework for forward rates.
The study shows how nonnegative Ricci curvature and metric cones imply the existence of abelian subgroups in the fundamental group of open manifolds.
problem Understanding the structure of fundamental groups of open manifolds with specific curvature properties.
method Analyzing the properties of the Riemannian universal cover and its asymptotic cones.
result The fundamental group of an open manifold with nonnegative Ricci curvature and certain geometric properties contains an abelian subgroup of finite index.
Finite-dimensional spaces of biharmonic functions on manifolds are explored.
problem Characterizing biharmonic functions on open manifolds with nonnegative Ricci curvature.
method Analyzing bounded and polynomial growth biharmonic functions, deriving Weyl bounds, and studying fourth-order operators.
result Finite-dimensional spaces of biharmonic functions with polynomial growth are established.
The abstract discusses open data resources for studying and controlling the spread of COVID-19.
problem Understanding and controlling the spread of COVID-19.
method Identification and description of open data resources and data-driven methodologies.
result Identification of variables and open data resources for analyzing COVID-19.
Study improves convergence rates for GVI under prior misspecification.
problem Improving convergence rates for GVI under prior misspecification.
method Proves rates of convergence and robustness to prior misspecification in GVI framework.
result Establishes sufficient conditions for existence and uniqueness of GVI posteriors.
Automated prediction of public speaking performance enables novel systems for tutoring public speaking skills. We use the largest open repository---TED Talks---to predict the ratings provided by the online viewers. The dataset contains over 2200 talk transcripts and the associated meta information including over 5.5 mi…
This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -We establish new minimax-rates for active learning under common \textit{noise conditions}. These rates display interesting transitions -- due to the inte…
We decompose the exchange rates returns of 41 currencies (incl. gold) into their sign and amplitude components. Then we group together all exchange rates with a common base currency, construct Minimal Spanning Trees for each group independently, and analyze properties of these trees. We show that both the sign and the …
We present the first adaptive strategy for active learning in the setting of classification with smooth decision boundary. The problem of adaptivity (to unknown distributional parameters) has remained opened since the seminal work of Castro and Nowak (2007), which first established (active learning) rates for this sett…
Derives equations for life insurance reserves with interest rate uncertainty.
problem Life insurance reserves with stochastic interest rates.
method Partial differential equations for reserves under stochastic interest rates.
result Explicit solutions for reserves under specific models.
The paper tackles fast rates in structured prediction problems.
problem Structured prediction problems with discrete outputs.
method Introducing continuous surrogate problems and leveraging their convergence rates for discrete problems.
result Super fast rates, including exponential rates, for excess risk in structured prediction problems.
We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and show that the validity of these assumptions - existence of a homogeneous genera…
The study examines spectral properties of the Laplacian on forms for open Riemannian manifolds.
problem Investigating spectral properties of the Laplacian on forms for open Riemannian manifolds.
method Finding sufficient conditions for the Weyl criterion to hold for the Lp-spectrum of the Laplacian on k-forms, proving the decomposition of the Lp-spectrum, and analyzing the resolvent set of the Laplacian. result The Lp-spectrum of the Laplacian on k-forms over hyperbolic space is described in detail. Improved Frank-Wolfe algorithm for generalized self-concordant functions converges quickly.
problem Efficiently solving learning problems with generalized self-concordant objectives.
method Simple Frank-Wolfe variant with open-loop step size strategy γt=2/(t+2). result Achieves O(1/t) convergence rate for primal and Frank-Wolfe gaps. Tian and Yau constructed a complete Ricci-flat Kähler metric on the complement of an ample and smooth anticanonical divisor. We inquire into the behaviour of this metric towards the boundary divisor and prove a slow decay rate of the difference to an appropriate explicitely given referential metric.
The paper models SOFR and EFFR dynamics, reconciling diffusive and piecewise paths.
problem Updating interest rate models for SOFR, which is becoming a key benchmark.
method Calibrates a model to SOFR and EFFR futures prices, reconciling diffusive and piecewise paths.
result The model reflects key empirical features of SOFR dynamics and reconciles diffusive and piecewise paths.
Investigates RI strategies for life insurers with LRD mortality rates.
problem Effect of long-range dependent mortality rates on RI strategies.
method Volterra mortality model, compound Poisson process, open-loop equilibrium mean-variance criterion.
result Explicit equilibrium RI controls derived and uniqueness studied.
New method for private linear regression under privacy constraints, achieving optimal rates.
problem Statistical complexity of private linear regression under unknown, ill-conditioned covariates.
method Information-Weighted Regression method
result Optimal convergence rates for both central and local privacy models.
SGDM accelerates faster than SGD with large batch sizes and permits broader learning rates.
problem Understanding the role of momentum in SGDM and its convergence rates.
method Analysis of SGDM convergence rates under strongly convex settings, including finite-sample rates and asymptotic normality of the averaged estimator.
result SGDM converges faster than SGD with large batch sizes and permits broader learning rates.
FedSight AI predicts federal funds rate using LLMs and multi-agent reasoning.
problem Predicting Federal Open Market Committee's decisions on federal funds rate.
method Multi-agent framework with large language models, structured and unstructured inputs, and CoD extension for efficient reasoning.
result Achieved 93.75% accuracy and 93.33% stability in predicting FOMC outcomes.
Paper analyzes convergence rate of noisy Bayesian Optimization with Expected Improvement.
problem Theoretical convergence behaviors and rates of Expected Improvement (EI) in Bayesian optimization.
method Analyzes Expected Improvement (EI) under Gaussian process (GP) prior assumption, considering noisy observations.
result Established asymptotic error bound and rate for GP-EI with noisy observations.
We investigate the dynamical and convergent properties of stochastic gradient descent (SGD) applied to Deep Neural Networks (DNNs). Characterizing the relation between learning rate, batch size and the properties of the final minima, such as width or generalization, remains an open question. In order to tackle this pro…
Chronos models improve financial forecasting by integrating multivariate data.
problem Improving financial forecasting accuracy using multivariate data.
method Evaluation of Chronos-2 on multivariate and univariate financial forecasting models.
result Multivariate forecasts consistently outperform univariate forecasts, especially for interest rates.
This work analyzes the convergence rate of unrolling for optimizing quadratic objectives.
problem The challenge of accurately computing Jacobians through optimization.
method Non-asymptotic convergence-rate analysis of unrolled differentiation for gradient descent and Chebyshev method.
result There is a trade-off between fast asymptotic convergence and immediate but slower convergence due to the learning rate.
Credit risk may be warehoused by choice, or because of limited hedging possibilities. Credit risk warehousing increases capital requirements and leaves open risk. Open risk must be priced in the physical measure, rather than the risk neutral measure, and implies profits and losses. Furthermore the rate of return on cap…
New research shows fixed-budget best-arm identification cannot match static oracle performance.
problem Fixed-budget best-arm identification's performance limitations.
method Analysis of various adaptive and static algorithms for best-arm identification.
result For any algorithm, there exists at least one instance where the error decay rate is at most \((1 + \frac{\log(K)}{8})^{-1}\) times that of the static oracle.
Improved sampling for Bayesian neural networks reduces vanishing acceptance rates and increases predictive accuracy.
problem Sampling inefficiency in Bayesian neural networks, especially with deep architectures and large datasets.
method Approximate blocked Gibbs sampling to partition and sample subgroups of parameters.
result Increased predictive accuracy and quantification of predictive uncertainty in classification tasks.
The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.
problem Stability and convergence rates of entropic and Sinkhorn potentials.
method Semiconcavity properties of entropic potentials and Schrödinger bridges.
result Exponential convergence rates for gradient and Hessian of Sinkhorn iterates.
New methods for skill rating in sports using state-space models.
problem Improving skill rating in competitive sports.
method State-space models, sequential Monte Carlo, discrete hidden Markov models.
result Advantages of state-space models for time-varying player skills.
OptiNet achieves near-minimax error rates with compression in Euclidean space.
problem Error and compression rates in non-parametric multiclass classification.
method Compression-based learning rule OptiNet and a novel general compression scheme.
result OptiNet achieves non-trivial compression rates with near-minimax error rates in Euclidean space.