Estimates natural parameters of p-tensor Ising models efficiently.
problem Estimating natural parameters of p-tensor Ising models from a single sample.
method Maximum pseudo-likelihood (MPL) method.
result MPL estimate is sqrt(N)-consistent under various conditions.
This paper improves multi-label ranking by reweighting univariate losses, enhancing consistency and performance.
problem Improving multi-label ranking performance while maintaining consistency.
method Systematic study of consistency and generalization error bounds for learning algorithms, proposing a reweighted univariate loss.
result Inconsistent pairwise losses can lead to better performance than consistent univariate losses in practice.
Improved estimators for causal inference using cross-fitting and undersmoothing.
problem Estimating expected conditional covariance in causal inference.
method Double cross-fit doubly robust (DCDR) estimators with undersmoothing for non-smooth nuisance functions.
result DCDR estimators achieve n \sqrt{n} n -consistency and asymptotic normality under minimal conditions. Improved SIR algorithm identifies effective factors more accurately.
problem Identifying significant factors with lower intrinsic dimensionality.
method Overlapping Sliced Inverse Regression (OSIR) algorithm.
result OSIR algorithm estimates effective dimension reduction space and number of effective factors more accurately.
Improved nonparametric regression with debiasing for root-n consistency.
problem Challenges in achieving root-n consistency and normal distribution for nonparametric estimators.
method Debiasing technique by adding a correction term to nonparametric estimators.
result Achieves root-n consistency and asymptotic normality.
A new law limits kurtosis contrast in balanced mixtures.
problem Kurtosis-based ICA fails in wide, balanced mixtures.
method Proved a redundancy law and showed purification restores contrast.
result Kurtosis contrast obeys O ( κ max / R e f f ) O(κ_{\max}/R_{\mathrm{eff}}) O ( κ m a x / R eff ) in balanced mixtures. Subbagging estimation for big data reduces memory usage while maintaining statistical consistency.
problem Memory constraints in analyzing massive datasets.
method Randomly subsample the data, aggregate estimators from subsamples, and use incomplete U-statistics theory.
result Subbagging estimator achieves N \sqrt{N} N -consistency and asymptotic normality under certain conditions. The paper tackles machine unlearning by designing efficient algorithms for adaptive query classes.
problem Designing efficient unlearning algorithms for machine learning models.
method Formalizes the problem and gives efficient unlearning algorithms for linear and prefix-sum query classes.
result Improved guarantees for stochastic convex optimization with reduced unlearning query complexity.
In this paper, we develop a 4/2 stochastic volatility plus jumps model, namely, a new stochastic volatility model including the Heston model and 3/2 model as special cases. Our model is highly tractable by applying the Lie symmetries theory for PDEs, which means that the pricing procedure can be performed efficiently. …
Estimating the leading principal components of data, assuming they are sparse, is a central task in modern high-dimensional statistics. Many algorithms were developed for this sparse PCA problem, from simple diagonal thresholding to sophisticated semidefinite programming (SDP) methods. A key theoretical question is und…
Improved kernel Stein discrepancy for large-scale data.
problem Efficiently testing probability distributions with kernel methods.
method Nyström approximation to reduce runtime complexity.
result Nyström-based KSD is n \sqrt{n} n -consistent and applicable for large datasets. The paper develops inference methods for high-dimensional multi-task regression with row-sparse coefficients.
problem Inference for high-dimensional multi-task regression with unknown coefficient matrix under row-sparsity.
method Proposes chi-square and normal inference methodologies using MT Lasso with de-biasing scheme and interaction matrix.
result Derives asymptotic normal and chi-square distribution results for valid confidence intervals and ellipsoids.
Proof of a simpler orthogonal double machine learning method.
problem Consistency and asymptotic normality of machine learning estimates.
method Alternative proof for Z-estimator in simpler setting.
result Orthogonal moments and consistency imply asymptotic normality.
CMOSS algorithm reduces regret in combinatorial semi-bandits with efficient computation.
problem Efficiently solving combinatorial semi-bandit problems with minimal regret.
method CMOSS algorithm achieves optimal regret bounds with minimal computational overhead.
result CMOSS achieves optimal regret bounds with minimal computational overhead.
This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be difficult to implement due to the potentially high computation complexity of the proj…
We give a comprehensive theoretical characterization of a nonparametric estimator for the L 2 2 L_2^2 L 2 2 divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is n \sqrt{n} n -consistent provided the densities are sufficiently smooth. In this smooth regime, we t…
Paper introduces a new histogram estimator for nonparametric density estimation that improves performance.
problem Smoothness-based nonparametric density estimators are not optimal for all types of data.
method Incorporates a multi-view latent variable model into histogram-style estimators.
result A new histogram estimator converges faster to multi-view models in L 1 L^1 L 1 error. Max-min margin Markov networks improve consistency in structured prediction.
problem Statistical inconsistency in max-margin methods for structured prediction.
method Defining a max-min margin formulation to overcome statistical inconsistency.
result Proves consistency and provides an explicit algorithm with finite sample generalization bounds.
Improved POMDP regret to sqrt(T) with known observation model.
problem Average-reward POMDPs with unknown transition model but known observation model.
method Optimistic algorithm using deterministic policies and novel estimation techniques.
result First approach with regret guarantee of sqrt(T) against optimal policy.
In this paper we consider the Allen-Cahn equation $$ -Δu = u-u^3 \ \mbox{in} \ {\mathbb R}^3 $$ We prove that for each k ∈ ( 2 , + ∞ ) , k\in\left( \sqrt{2},+\infty\right), k ∈ ( 2 , + ∞ ) , there exists a solution to the equation which has growth rate k k k , i.e. ∥ u − H ( ⋅ − k ln r + c k ) ∥ L ∞ → 0 \| u-H(\cdot -k \ln r + c_k) \|_{L^\infty} \to 0 ∥ u − H ( ⋅ − k ln r + c k ) ∥ L ∞ → 0 The main ingredients of our proof con…
Study learns dynamics of linear systems from multiple short trajectories.
problem Learning dynamics of autonomous linear systems from multiple short trajectories.
method Finite sample analysis for stable and unstable systems, adjusting trajectory length for marginally stable systems.
result Learning rate of O ( 1 N ) \mathcal{O}(\frac{1}{\sqrt{N}}) O ( N 1 ) for both stable and unstable systems. Improves machine learning consistency with orthogonal moment equations.
problem Improving consistency of machine learning estimates with complex nuisance parameters.
method Employing Neyman-orthogonal moment equations to improve consistency from n − 1 / 4 n^{-1/4} n − 1/4 to n − 1 / ( 2 k + 2 ) n^{-1/(2k+2)} n − 1/ ( 2 k + 2 ) . result Second-order orthogonality can improve consistency to n − 1 / ( 2 k + 2 ) n^{-1/(2k+2)} n − 1/ ( 2 k + 2 ) . New framework improves efficiency in low-rank matrix bandit problems.
problem Stochastic contextual low-rank matrix bandit problem with unknown rank matrices.
method G-ESTT and G-ESTS frameworks using Stein's method and regularization.
result Achieved improved regret bounds for low-rank matrix bandit problems.
The paper analyzes matrix completion with unlabeled implicit feedback and provides error bounds.
problem Matrix completion with shared low-rank ground truth and sampling distribution.
method Combining subspace recovery theory and matrix completion bounds.
result Error bounds showing contributions from estimating the sampling distribution and ground truth.
New bounds on efficiency for conformalized regression methods.
problem Efficiency of conformal prediction in regression models.
method Non-asymptotic bounds on prediction set length for conformalized quantile and median regression.
result Identifies phase transitions in convergence rates across different regimes of miscoverage level.
New algorithms improve on consistency and robustness in convex function chasing with black-box advice.
problem Minimizing cost in normed vector space with black-box advice for convex function chasing.
method Two novel algorithms: INTERP and BDINTERP, exploiting convexity to achieve improved consistency and robustness.
result BDINTERP achieves near-optimal consistency-robustness trade-off for α-polyhedral cost functions.
The paper analyzes k k k -means clustering for missing data, proving statistical guarantees under MCAR.
problem Statistical guarantees for k k k -means clustering with missing data, especially under Missing Completely at Random (MCAR). method Established n \sqrt{n} n -excess risk bound and consistency of cluster centers under general missing mechanisms; derived n \sqrt{n} n -convergence rate and asymptotic normality for MCAR. result Achieving n \sqrt{n} n -rate and converging to true cluster centers requires distinct true cluster centers in every dimension under MCAR. The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on t…
The paper explores the shape of filling-systole subspace in surface moduli space and critical points of systole function.
problem Understanding the structure and critical points of the filling-systole subspace in surface moduli space.
method Analyzing Teichmüller and Weil-Petersson distances to determine the proximity of points to the subspace.
result Most points in M g \mathcal{M}_g M g are within a specific Teichmüller distance from X g X_g X g and have a certain distance from the thick part of M g \mathcal{M}_g M g . The paper proves formulas and theorems for specific operators on manifolds.
problem Analyzing operators on manifolds and proving theorems.
method Obtained Lichnerowicz type formulas and proved Kastler-Kalau-Walze theorems.
result Proved Kastler-Kalau-Walze type theorems for specific operators.
We formalize AURC and develop estimators for SC systems.
problem Evaluation of SC systems' performance.
method Formal statistical formulation, Monte Carlo methods, plug-in estimators.
result Plug-in estimators are consistent, with low bias and bounded MSE.
New RL algorithm reduces regret in finite-horizon episodic tasks.
problem Minimizing regret in model-based reinforcement learning.
method Optimism principle applied to value-targeted regression.
result Regret bound of i l d e O ( d H 3 T ) ilde{\mathcal{O}}(d\sqrt{H^{3}T}) i l d e O ( d H 3 T ) for linear mixtures. MR estimator simplifies causal inference by combining models without hyperparameter tuning.
problem Difficulty in choosing optimal hyperparameters for neural network models in causal inference.
method Multiply Robust (MR) estimator that combines multiple first-step models.
result MR estimator is n r n^r n r consistent and asymptotically normal under certain conditions. Given an Einstein structure with positive scalar curvature on a four-dimensional Riemannian manifolds, that is R i c = λ g Ric=λg R i c = λ g for some positive constant λ λ λ . For convenience, the Ricci curvature is always normalized to R i c = 1 Ric=1 R i c = 1 . A basic problem is to classify four-dimensional Einstein manifolds with positive or nonnegative cu…
Reservoir computing's success depends on mapping different input time series to separable states.
problem Quantifying the ability of random linear reservoirs to map different input time series.
method Mathematical framework using spectral properties of the connectivity matrix.
result Separation capacity is fully characterized by the spectral properties of the connectivity matrix.
The paper confirms Yau's conjecture for minimal rotational hypersurfaces.
problem Yau's conjecture about the minimal area of certain hypersurfaces.
method Analyzes minimal rotational hypersurfaces to confirm the conjecture.
result The area of compact minimal rotational hypersurfaces is either equal to the unit sphere's area or another specific value.
Paper improves Bayesian regret bounds for Thompson Sampling in reinforcement learning.
problem Improving Bayesian regret bounds for Thompson Sampling in reinforcement learning.
method Using a discrete set of surrogate environments and posterior consistency analysis, the authors derive an upper bound of order O ( H d l 1 T ) O(H\sqrt{d_{l_1}T}) O ( H d l 1 T ) . result The derived upper bound of O ( H d l 1 T ) O(H\sqrt{d_{l_1}T}) O ( H d l 1 T ) is a significant improvement over previous bounds. The paper improves bounds on the shortest closed geodesic length on surfaces.
problem Finding the shortest closed geodesic on surfaces of finite area.
method Proving new upper bounds for the length of the shortest closed geodesic.
result Improved bounds on the length of the shortest closed geodesic.
The paper bounds eigenvalues and integrals of eigenfunctions on hyperbolic manifolds.
problem Eigenvalues and integrals of eigenfunctions on compact hyperbolic manifolds.
method Spectral decompositions and consistency conditions derived from quadruple overlap integrals.
result Upper bounds on Laplacian eigenvalues and triple overlap integrals.
Develops new methods for causal inference from observational data.
problem Improving causal inference from observational studies.
method Generalized Optimal Matching (GOM) framework.
result GOM methods provide a unified theory for optimal matching, covariate balancing, and doubly-robust methods.
New algorithm reduces regret and constraint violation in online convex optimization with complex constraints.
problem Online convex optimization with multiple functional constraints and a simple constraint set.
method Instance-dependent bound using online primal-dual mirror-prox algorithm in general normed spaces.
result Achieves an O(√V*(T)) regret and O(1) constraint violation, improving over previous works.
Let M n M^n M n be a compact hypersurface with constant mean curvature H H H in S n + 1 \mathbb{S}^{n+1} S n + 1 . Denote by S S S the squared norm of the second fundamental form of M M M . We prove that there exists a positive constant γ ( n ) γ(n) γ ( n ) depending only on n n n such that if ∣ H ∣ ≤ γ ( n ) |H|\leqγ(n) ∣ H ∣ ≤ γ ( n ) and β ( n , H ) ≤ S ≤ β ( n , H ) + n 23 β(n,H)\leq S\leqβ(n,H)+\frac{n}{23} β ( n , H ) ≤ S ≤ β ( n , H ) + 23 n , then $S\equi…
Study Thompson Sampling in adversarial bit prediction, finding regret bounds and optimal sequences.
problem Adversarial bit prediction with varying error weights.
method Thompson Sampling, analyzing sequences with largest and smallest regret.
result Regret bounds for adversarial bit prediction sequences, including optimal and worst-case scenarios.
Study identifies and validates a method for system identification of Markov jump linear systems.
problem System identification for autonomous Markov jump linear systems with complete state observations.
method Proposes switched least squares method for identification and derives rates of convergence.
result Data-independent rate of convergence is O ( log ( T ) / T ) \mathcal{O}\big(\sqrt{\log(T)/T} \big) O ( log ( T ) / T ) , showing strong consistency. New algorithm reduces constraint violation to O ( T 1 / 3 ) O(T^{1/3}) O ( T 1/3 ) while maintaining O ( T ) O(\sqrt{T}) O ( T ) regret.
problem Minimizing static regret and cumulative constraint violation in constrained online convex optimization.
method Proposes an algorithm that achieves O ( T ) O(\sqrt{T}) O ( T ) regret and O ( T 1 / 3 ) O(T^{1/3}) O ( T 1/3 ) cumulative constraint violation. result Shows that O ( T 1 / 3 ) O(T^{1/3}) O ( T 1/3 ) cumulative constraint violation is achievable with O ( T ) O(\sqrt{T}) O ( T ) regret. Contextual bandits study how reward variance affects regret bounds.
problem Investigating how small reward variance impacts regret bounds in contextual bandits.
method Analyzing two types of adversaries and function approximation complexities.
result Regret bounds are influenced by the eluder dimension and reward variance.
New method estimates discrete distributions while protecting privacy.
problem Estimating discrete distributions with local differential privacy.
method Combining robust learning and local differential privacy.
result Minimax estimation rate of ε d / α 2 k + d 2 / α 2 k n ε\sqrt{d/α^2 k}+\sqrt{d^2/α^2 kn} ε d / α 2 k + d 2 / α 2 k n under privacy constraint. We use Khovanov homology to define families of LDPC quantum error-correcting codes: unknot codes with asymptotical parameters [[3^(2l+1)/sqrt(8πl);1;2^l]]; unlink codes with asymptotical parameters [[sqrt(2/2πl)6^l;2^l;2^l]] and (2,l)-torus link codes with asymptotical parameters [[n;1;d_n]] where d_n>\sqrt(n)/1.62.