A clustering algorithm for natural hierarchical clusters with near-linear time complexity.
problem Hierarchical clustering with near-linear time complexity.
method Nearest neighbor based clustering algorithm that defines clusters naturally.
result Near-linear time and space complexity for certain datasets.
In this work, we propose a robust approach to design distributed controllers for unknown-but-sparse linear and time-invariant systems. By leveraging modern techniques in distributed controller synthesis and structured linear inverse problems as applied to system identification, we show that near-optimal distributed con…
Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.
problem Gaussian mean estimation and linear regression with Gaussian covariates in the presence of Huber contamination.
method Near-optimal algorithms with optimal error guarantees, achieving sample complexity n = i l d e O ( d / ε 2 ) n = ilde{O}(d/ε^2) n = i l d e O ( d / ε 2 ) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
New framework for DP-SMO with near-optimal privacy-loss trade-off.
problem Optimal trade-off between privacy and population loss in DP-SMO.
method General framework using Phased-ERM method and black-box optimization.
result Near-linear time algorithms with near-optimal guarantees.
New method for robust linear regression in nearly linear time.
problem High-dimensional robust linear regression with adversarial corruption.
method Proposes estimators for two settings with near linear time complexity.
result Achieves optimal sample complexities and recovery guarantees.
CTT compresses samples to test distributions near-linearly, outperforming existing methods.
problem Efficiently testing distributions with high power and near-linear runtime.
method Sample compression followed by permutation testing.
result CTT achieves near-linear runtime while maintaining high statistical power.
New algorithm speeds up Gaussian process optimization.
problem Scalability issues in Gaussian process optimization.
method BBKB (Batch Budgeted Kernel Bandits) algorithm that selects candidates in batches and adaptively delays updates.
result Provable near-linear time complexity and significant speedup over existing methods.
Unified method for estimating properties of large domain distributions efficiently.
problem Estimating properties of distributions over large domains efficiently.
method Piecewise-polynomial approximation technique for constructing sample- and time-efficient estimators.
result Near-linear-time computable estimators with optimal and highly-concentrated approximation values.
New algorithm approximates distributions with near-linear time and optimal sample efficiency.
problem Approximating distributions from samples efficiently and accurately.
method Near-linear-time estimator for distributions using universal polynomial approximation.
result Establishes c t , d = 2 c_{t,d}=2 c t , d = 2 for all ( t , d ) e ( 1 , 0 ) (t,d)
e(1,0) ( t , d ) e ( 1 , 0 ) , achieving optimal approximation. Compress++ speeds up distribution compression to near-linear time.
problem Accurately summarize a probability distribution using a small number of points efficiently.
method Introduces Compress++, a meta-procedure to speed up any thinning algorithm.
result Achieves n \sqrt{n} n points with O ( log n / n ) \mathcal{O}(\sqrt{\log n/n}) O ( log n / n ) integration error in O ( n log 3 n ) \mathcal{O}(n \log^3 n) O ( n log 3 n ) time and O ( n log 2 n ) \mathcal{O}( \sqrt{n} \log^2 n ) O ( n log 2 n ) space. Improved efficient robust regression with near-linear time and subquadratic samples.
problem Robust linear regression with unknown covariance matrix under Gaussian covariates.
method Near-linear time algorithm using subquadratic samples, complemented by SQ and polynomial lower bounds.
result Achieves prediction error O ( ε κ ) O(\sqrt{εκ}) O ( ε κ ) for ε κ ≲ 1 εκ\lesssim 1 ε κ ≲ 1 , improving over prior works. Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance, it is unknown whether general optimal transport distances can be approximated in …
New algorithms combat adversarial attacks in stochastic linear bandits.
problem Adversarial attacks on stochastic linear bandit rewards.
method Two variants of Robust Phased Elimination algorithms, one knowing C C C and one not. result Near-optimal regret in non-corrupted case and additive terms dependent on C C C . Quantum algorithms reduce clustering input size, achieving near-linear approximation.
problem Efficiently clustering large datasets in quantum computing.
method Quantum coresets for k k k -clustering with sublinear query complexity. result Achieves near-linear approximation for k k k -clustering with coresets. New algorithm trains neural networks in near-linear time, overcoming slow convergence issues.
problem Slow convergence and computational overhead in training deep neural networks.
method Reformulates Gauss-Newton iteration as an ℓ2-regression problem and uses Fast-JL dimension reduction.
result Achieves an O(mn)-time algorithm for training ReLU networks, near-linear in dimension.
Improved Sinkhorn algorithm for UOT with near-linear complexity.
problem Solving the entropic regularized Unbalanced Optimal Transport problem efficiently.
method Geometric convergence analysis of Sinkhorn updates and primal solution properties.
result Near-linear time complexity for finding ε \varepsilon ε -approximate UOT solutions. Many important applications, including signal reconstruction, parameter estimation, and signal processing in a compressed domain, rely on a low-dimensional representation of the dataset that preserves {\em all} pairwise distances between the data points and leverages the inherent geometric structure that is typically p…
New method achieves near-optimal regret without simulator.
problem Adversarial linear contextual bandits with unknown loss vectors.
method Near-optimally reduces regret to sqrt(T) without simulator.
result Achieves regret of sqrt(T) without simulator, improving existing methods.
TiDE uses MLP for fast, simple long-term time-series forecasting.
problem Long-term time-series forecasting challenges.
method Time-series Dense Encoder (TiDE) based on MLP.
result TiDE matches or outperforms Transformer models while being 5-10x faster.
LinMED is a new linear bandit algorithm with near-optimal regret bound.
problem Optimizing decision-making in linear bandit problems with sub-Gaussian distributions.
method LinMED is a randomized linear bandit algorithm with closed-form arm sampling probabilities.
result LinMED achieves a near-optimal regret bound of d n d\sqrt{n} d n up to logarithmic factors. Analyzes Hessian spectrum for neural networks near optimal learning.
problem Understanding learning dynamics near optimal points in neural networks.
method Characterizes Hessian eigenspectrum for teacher-student problems, using analytical and numerical methods.
result The rank of the Hessian matrix determines effective number of parameters for non-linear networks.
Near-logarithmic regret per switch achieved for mixable/exp-concave losses.
problem Online optimization of mixable loss functions with dynamic environments.
method Online mixture framework using static solvers and hyper-expert creations.
result Near-logarithmic regret per switch with sub-polynomial complexity.
New algorithm reduces switching costs in RL beyond linear MDPs.
problem Costly policy switching in reinforcement learning.
method ELEANOR-LowSwitching algorithm for linear Bellman-complete MDPs.
result Achieves near-optimal regret with logarithmic switching cost.
This paper develops a fast algorithm for solving nonlinear PDEs using sparse Cholesky factorization.
problem Efficiently solving nonlinear PDEs with Gaussian processes and kernel methods.
method Sparse Cholesky factorization for near-linear complexity.
result Near-linear complexity algorithm for working with kernel matrices of nonlinear PDEs.
A single policy suffices for near-optimal parallel exploration in RL.
problem Quantitative effects of parallel exploration in reward-free RL.
method Using a single policy to guide exploration across all agents.
result Near-linear speedup and near-minimax optimality for linear MDPs.
We study the problem of regret minimization for distributed bandits learning, in which M M M agents work collaboratively to minimize their total regret under the coordination of a central server. Our goal is to design communication protocols with near-optimal regret and little communication cost, which is measured by the…
Local polynomial regression (Fan and Gijbels 1996) is an important class of methods for nonparametric density estimation and regression problems. However, straightforward implementation of local polynomial regression has quadratic time complexity which hinders its applicability in large-scale data analysis. In this pap…
Grokking occurs in simple binary logistic classification near linear separability and noise.
problem Delayed generalization in binary logistic classification.
method Analytical and empirical insights into gradient descent dynamics near critical points.
result Logistic regression exhibits grokking when training data is nearly linearly separable from the origin with strong noise.
Efficiently simulates the Heston model with large time steps using a novel method.
problem Challenges in simulating the Heston model with large time steps.
method Implicit integrated variance scheme exploiting the near-linear nature between stochastic driver and conditional integrated variance process.
result Achieves near-exact accuracy with coarse discretizations, efficient for large time steps.
New algorithm recovers sparse signals from linearly sparse dictionaries efficiently.
problem Recovering sparse signals from linearly sparse dictionaries.
method Spectral method on reweighted covariance matrices.
result First polynomial-time algorithm for near-linear sparsity in overcomplete dictionaries.
We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully overparameterize the class of LDSs by a polylogarithmic factor, in exchange for con…
We develop efficient algorithms for robust PCA that handle outliers.
problem Finding principal components in datasets with outliers.
method Nearly-linear time and streaming algorithms for robust PCA.
result Near-optimal error guarantees for robust PCA with nearly-linear time and memory usage.
We study the behavior of the critical price of an American put option near maturity in the exponential Lévy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the l…
Develops estimators for near-optimal linear regression under distribution shift.
problem Linear regression under distribution shift with scarce target domain data.
method Minimax linear risk estimators covering various transfer learning settings.
result Achieves near-optimal risk for linear regression problems under distribution shift.
New algorithms for differentially private optimization in convex and non-convex settings with near-optimal rates.
problem Differentially private optimization in convex and non-convex settings.
method Developed algorithms for convex and non-convex settings with near-optimal excess population risk.
result Achieved near-optimal rates in near-linear time for convex settings and nearly dimension independent rates for non-convex settings.
New method speeds up NIR spectroscopy calibration by 400x.
problem Efficient preprocessing selection in NIR spectroscopy.
method Operator-adaptive PLS and Ridge regression.
result Significant reduction in fitting time with comparable prediction quality.
In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the ti…
LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.
problem Computational bottleneck in randomization step for large-scale linear algebra.
method Near constant-time linear random projections from LightOn OPUs.
result Significant acceleration of RandNLA algorithms with negligible precision loss.
Noise makes learning linear thresholds hard, but algorithms can still learn near-optimal thresholds.
problem Learning linear thresholds in noisy data.
method Exploiting natural assumptions on data-generating process.
result Efficient learning of near-optimal linear thresholds is still possible with small data even in the presence of noise.
Paper proposes FedQ-Advantage for federated Q-learning with near-optimal regret and low communication cost.
problem Near-optimal federated Q-learning with low communication cost.
method Reference-advantage decomposition for variance reduction, synchronization between agents and server, policy update.
result Achieves almost optimal regret and near-linear regret speedup compared to single-agent learning.
Symbolic grounding in causal dynamics achieves near-infinite temporal consistency.
problem Achieving linear identifiability in non-Gaussian physical systems.
method Physics-Grounded Symbolic Architecture (PGSA)
result PGSA achieves exact linear identifiability for all physical regimes.
Study cost-driven state representation learning for control from partial observations.
problem Learning state representation for control from partial and high-dimensional observations.
method Cost-driven state representation learning via predicting cumulative costs.
result Established finite-sample guarantees for near-optimal representation and controller.
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the interpretability of the features. We study the problem of constructing optimal sparse linear a…
We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping properties of the corresponding biharmonic heat operator on certain Banach spaces. Thi…
New algorithms for model selection in linear bandits adapt to instance complexity.
problem Adapting to the instance-dependent complexity of the true model in linear bandits.
method Design of algorithms in fixed confidence and fixed budget settings, leveraging experimental design and selection-validation procedures.
result Near instance optimal guarantees for model selection in linear bandits.
New approach achieves optimal rates for differentially private stochastic convex optimization with heavy-tailed gradients.
problem Differentially private stochastic convex optimization with heavy-tailed gradients.
method Reduction-based approach to achieve optimal rates.
result Achieved optimal rates up to logarithmic factors, nearly matching a lower bound.
Direct proof shows adaptive gradient descent converges near-linearly for convex functions.
problem Proving near-linear convergence of adaptive gradient descent for convex functions.
method Direct Lyapunov-based argument for convex functions with unique minimizer.
result Direct proof of near-linear convergence for convex functions.
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor γ ∈ ( 0 , 1 ) γ\in(0,1) γ ∈ ( 0 , 1 ) we provide an algorithm that computes an ε ε ε -optimal strategy with high-probability given $\tilde{O}((1 - γ)^{-3}…