Study fake projective planes using recent results to show bicanonical map is always an embedding and construct an exceptional collection.
problem Analyzing Keum's fake projective planes and their geometric properties.
method Apply recent results from Galkin et al. [GKMS15] to study fake projective planes.
result The bicanonical map of Keum's fake projective planes is always an embedding.
A quandle is a self-distributive algebraic structure that appears in quasi-group and knot theories. For each abelian group A and c \in A we define a quandle G(A, c) on \Z_3 \times A. These quandles are generalizations of a class of non-medial Latin quandles defined by V. M. Galkin so we call them Galkin quandles. Each …
Reply to Ogburn et al. on their critique of Wang and Blei's work.
problem Critique of Wang and Blei's work on the blessings of multiple causes.
method Discussion and clarification of Wang and Blei's claims and findings.
result Wang and Blei's premise is correct and there are no foundational errors.
ES and FD gradients converge as optimization dimension grows.
problem Understanding the relationship between Evolution Strategies and Finite Differences gradients.
method Analyzing the convergence of gradients as the optimization dimension increases.
result ES and FD gradients converge as the dimension of the vector under optimization increases.
We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the problem under three different assumptions for the feedback: full information, and the …
New method improves fairness in machine learning models.
problem Reducing bias in machine learning classification models.
method Formulated as multi-objective optimization, uses gradient descent-ascent algorithm with modified gradient update step.
result Empirical tests show improved fairness compared to state-of-the-art algorithms.
New interpolation methods outperform Gaussian smoothing in derivative-free optimization.
problem Optimizing functions with noisy evaluations and no derivative information.
method First-order line search methods using linear interpolation vs. Gaussian smoothing.
result Linear interpolation yields better convergence rates and performance.
In this small note we use results derived in Berestycki et al. to correct the celebrated formulae of Hagan et al. We derive explicitly the correct zero order term in the expansion of the implied volatility in time to maturity. The new term is consistent as β→1. Furthermore, numerical simulations show that it reduc…
Algorithm for sequential user-product rating prediction in recommender systems.
problem Predicting ratings in a sequential user-product rating prediction setting.
method Gamma process factor model with Thompson Sampling and Information-Directed Sampling.
result Information-Directed Sampling achieves state-of-the-art performance.
R package huge simplifies graph estimation for high-dimensional data.
problem Estimating high-dimensional undirected graphs from data.
method Uses recent results in literature, including recent graph estimation methods.
result Improves on existing package glasso by providing more features and better efficiency.
Study shows offline RL under Q⋆-approximation and partial coverage is harder than previously thought.
problem Theoretical limits of offline reinforcement learning under Q⋆-approximation and partial coverage. method Introduced a decision-estimation framework to decompose offline RL complexity into decision and value estimation errors.
result Answered the open question by proving sample inefficiency under partial coverage is not guaranteed by Q⋆-realizability and Bellman completeness. Algorithm combines RL and black-box optimization for policy learning.
problem Improving policy learning efficiency in RL.
method Combines actor-critic approach with stochastic search and parametric/local policy estimation.
result Demonstrates effectiveness on diverse RL tasks with limited compute.
Hard to estimate L2-accurate scores without strong assumptions.
problem Estimating the score of unknown data distributions accurately.
method Reduction to generating samples and leveraging lattice-based cryptography hardness.
result Score estimation is computationally hard even with polynomial sample complexity.
DAIS improves AIS by resampling, avoiding gradient issues.
problem Low effective sample size in DAIS.
method DAIS with resampling step to improve efficiency.
result Resampling step avoids gradient variance issues.
This paper corrects errors in UMAP's derivation and explains its properties.
problem Errors in UMAP's derivation by McInnes et al.
method Full derivation of Spivak's functors and McInnes et al.'s finite variant.
result Corrected errors and provided an explicit description of the metric realization.
New risk statistics for loss-based regulation.
problem Regulatory focus on losses over gains.
method Developed new risk statistics using scenario analysis.
result New risk statistics extend existing measures.
Research aims to ensure fair classification across explicit and implicit sensitive features.
problem Ensuring fairness in machine learning models when sensitive features are not explicitly provided.
method Defined explicit and implicit cohorts, used clustering of embeddings, modified loss function.
result Improved classification parity across explicit and implicit sensitive features.
We identify 'critical windows' in diffusion models where specific features emerge, providing a theoretical framework.
problem Understanding narrow time intervals in diffusion models where specific features emerge.
method Developed a formal framework to study these critical windows, showing provable bounds for certain data types.
result Proved that critical windows can be bounded in terms of measures of separation for data from mixtures of log-concave densities.
New estimator stabilizes higher-order influence functions for stable statistical inference.
problem Numerical instability in estimating inverse population Gram matrix.
method Proposes a new stabilized higher-order estimator without sample splitting.
result Stabilized estimator exhibits more stable performance and similar statistical guarantees.
Mirror Langevin Algorithm converges with zero bias.
problem Achieving convergence with zero bias in discrete-time sampling.
method Discretization of Mirror Langevin Diffusion and mean-square analysis.
result Mirror Langevin Algorithm converges with zero bias.
Stable ResNet stabilizes gradients in deep networks.
problem Gradient vanishing and exploding in deep ResNet architectures.
method Introducing Stable ResNet architectures with gradient stabilization and infinite depth expressivity.
result Stable ResNet maintains gradient stability and expressivity in deep networks.
New estimator stabilizes higher-order influence functions for bilinear forms.
problem Stability issues in estimating bilinear forms using higher-order influence functions.
method Proposes a new stabilized higher-order estimator for a class of bilinear forms without sample splitting.
result New estimator exhibits more stable finite-sample performance compared to the empirical higher-order estimator.
AI models help solve a symplectic topology problem.
problem Lagrangian smoothability question from Abouzaid et al.
method Used large language models (LLM) to approach the problem.
result Suggested new constructions in polyhedral symplectic topology.
Generative models improve commodity hedging using deep learning.
problem Improving risk management in commodity markets.
method Four state-of-the-art generative models adapted for commodity time series.
result Deep hedging of commodity options trained on generated time series shows promising results.
New SMC methods improve likelihood estimates for doubly intractable models.
problem Bayesian inference for models with intractable partition functions.
method Marginal sequential Monte Carlo with adaptive likelihood estimates.
result Improved likelihood estimates lead to more accurate inference.
New methods improve inference after prediction without strong model assumptions.
problem Improper inference after prediction can lead to invalid results.
method Angelopoulos et al. (2023) and Wang et al. (2020) propose corrections to inference.
result Angelopoulos et al. method controls type 1 error and provides correct coverage.
This paper analyzes convergence rates of neural networks in the deep learning regime.
problem Understanding convergence rates of neural networks in the deep learning regime.
method Analyzing the Neural Tangent Kernel (NTK) convergence rates in the large depth limit.
result Quantifies the impact of initialization and activation function on NTK convergence rates.
New model selects robustly in adversarial reinforcement learning with unknown corruption.
problem Adversarial corruption in reinforcement learning with unknown total corruption amount.
method Model selection approach for finite-horizon tabular and linear MDPs.
result First worst-case optimal bound without knowledge of total corruption.
ABC method uses MCMC for likelihood estimation.
problem Likelihood estimation for complex models.
method Approximate Bayesian Computation (ABC) with MCMC.
result MCMC can be seen as ABC for likelihood estimation.
Piecewise normalizing flows improve multi-modal distribution modeling.
problem Improving accuracy in modeling multi-modal distributions.
method Divide target distribution into clusters, train flows to match standard normal base.
result Piecewise flows outperform standard approaches in accuracy.
New algorithms reduce matching market regret to log(T) with improved stability.
problem Minimizing regret in two-sided matching markets with bandit feedback.
method Phase-based algorithm with local arm deletion to improve stability.
result Achieves Θ(log(T)) regret for markets with uniqueness consistency.
We improve adversarial robustness calibration analysis for broader hypothesis sets.
problem Improving calibration for adversarial robustness in machine learning.
method A finer definition of calibration for adversarial robustness.
result Our results cover most common hypothesis sets in machine learning.
The paper analyzes and improves a deep learning optimization technique using matrix gradient orthogonality.
problem Improving deep learning training through more effective optimization methods.
method Develops a stochastic non-Euclidean trust-region gradient method for deep learning optimization.
result Proves state-of-the-art convergence results for the proposed algorithm in various scenarios.
Deep Q-learning methods are sensitive to time discretization, which this paper addresses.
problem Sensitivity of Deep Q-learning methods to time discretization in near continuous-time environments.
method Identified and formalized the problem of sensitivity to time discretization. Developed a principled off-policy RL algorithm.
result Proved that Q-learning does not exist in continuous time and developed a robust algorithm.
Study proves NN matching is equivalent to Riesz regression for debiased machine learning.
problem Addressing bias in machine learning models.
method Interprets NN matching as Riesz regression and derives it from LSIF.
result NN matching is shown to be equivalent to Riesz regression.
Work establishes conditions for bias-free policy optimization.
problem Improving policy optimization methods without introducing bias.
method Established conditions for parametric critic without bias.
result Identified bias in current policy optimization algorithms.
This comment reexamines Simard et al.'s work in [D. Simard, L. Nadeau, H. Kroger, Phys. Lett. A 336 (2005) 8-15]. We found that Simard et al. calculated mistakenly the local connectivity lengths Dlocal of networks. The right results of Dlocal are presented and the supervised learning performance of feedforward neural n…
EWC uses quadratic penalties that may double-count earlier task data.
problem Catastrophic forgetting in neural networks.
method Extended derivation of EWC with multiple tasks.
result Quadratic penalties in EWC might double-count earlier task data.
Paper presents an efficient algorithm for linear MDP with low switching cost.
problem Large state space reinforcement learning problems with low switching cost.
method First algorithm for linear MDP with low switching cost, achieving near-optimal regret and switching cost.
result Regret bound of $\widetilde{O}\left(\sqrt{d^3H^4K}
ight)$ and near-optimal switching cost of $O\left(d H\log K
ight)$.
The paper reviews methods for determining the number of communities in network data.
problem Determining the number of communities in network data.
method Statistical methods for hypothesis testing and clustering in network models.
result SCORE and NCV methods evaluated for clustering in Degree-Corrected Block Models, with NCV facing challenges.
Study on convergence of OMD for saddle point problems, correcting previous claims.
problem Convergence of OMD for saddle point problems with exact gradients.
method Analysis of Mirror Descent and Optimistic Mirror Descent for saddle point problems.
result Monotone convergence only occurs after a large number of iterations for coherent saddle point problems.
Our article considers the class of recently developed stochastic models that combine claims payments and incurred losses information into a coherent reserving methodology. In particular, we develop a family of Heirarchical Bayesian Paid-Incurred-Claims models, combining the claims reserving models of Hertig et al. (198…
FOLKLORE algorithm speeds up online multiclass logistic regression.
problem Efficiently solving online multiclass logistic regression without high computational cost.
method Developed FOLKLORE algorithm with improved runtime and regret bound.
result First practical algorithm for online multiclass logistic regression.
New gradient estimators for discrete variables improve model training.
problem Training models with discrete latent variables is challenging due to high gradient variance.
method Introduced novel gradient estimators based on importance sampling and statistical couplings, extending to categorical variables.
result Proposed gradient estimators outperform previous methods in systematic experiments.
New algorithm fills gaps in offline data for hybrid RL, achieving similar gains without coverage assumptions.
problem Lack of provable benefits in hybrid RL with coverage assumptions.
method Warm-starting optimistic online algorithms with offline data in experience replay buffer.
result Hybrid RL gains similar to offline-only RL without coverage assumptions, demonstrating efficient exploration.
Two methods for quantile regression are compared and found to produce tighter intervals.
problem Comparing methods for producing prediction intervals in quantile regression.
method Two recently proposed methods combining conformal inference and quantile regression.
result Romano et al.'s method typically yields tighter prediction intervals in finite samples.
Improved privacy and efficiency in online convex optimization.
problem Differentially private online convex optimization in high dimensions.
method Improves upon Agarwal et al. [2023] by reducing dimension factors and removing smoothness requirement.
result Best known rates for (ε,δ)-differentially private online convex optimization in the regime of ε not being very small. An online convex matrix factorization algorithm with interpretable bases.
problem Scaling and interpretability in matrix factorization for large datasets.
method Online algorithm with representative data samples for interpretability.
result Significant computational savings compared to classical convex MF.