Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
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.
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 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 algorithm speeds up path computation for optimal models.
problem Finding the exact path of optimal models from a finite set.
method Dynamic programming approach for linear time computation.
result Dynamic programming achieves linear time for breakpoints computation.
Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the assignment problem typically requires cubic time and its pairwise computation is expen…
AuON is a linear-time optimizer that improves upon Muon's performance without approximate orthogonal matrices.
problem High memory and computational costs of orthogonal momentum updates.
method AuON uses normalized nonlinear scaling and a 'emergency brake' to handle exploding attention logits.
result AuON achieves strong performance without approximate orthogonal matrices, preserving structural alignment and reconditioning.
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.
LITE efficiently estimates Gaussian PoM with linear time and memory complexity.
problem Estimating the probability of maximality (PoM) of Gaussian vectors efficiently.
method LITE: entropy-regularized UCB approach for almost-linear time and memory complexity.
result Achieves state-of-the-art accuracy with significantly faster performance than existing methods.
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 algorithm achieves optimal privacy and efficiency in non-Euclidean convex optimization.
problem Optimizing convex functions while maintaining privacy in non-Euclidean settings.
method Developed a linear-time algorithm for ℓp-setups, leveraging geometric properties. result Optimal excess risk achieved in linear time for 1<p≤2. 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.
Linear-time graph optimization using reinforcement learning.
problem Solving combinatorial optimization problems on real-world graphs.
method Graph neural network trained with reinforcement learning.
result Approximate solutions in linear time for various graph problems.
New algorithms achieve optimal DP convex optimization with linear time and gradient computations.
problem Private stochastic convex optimization with optimal excess loss.
method Two new techniques: variable batch sizes and localization with stable optimization.
result Achieves optimal bound on excess loss with O(min{n,n2/d}) gradient computations. 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 ct,d=2 for all (t,d)e(1,0), achieving optimal approximation. 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=ildeO(d/ε2) and almost linear runtime. result First sample near-optimal and almost linear-time algorithms with optimal error guarantees for both problems.
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and time-efficient estimators for all sufficiently smooth, symmetric and non-symmetric, …
New algorithm selects best distribution privately in nearly-linear time.
problem Estimating the best distribution from samples under differential privacy constraints.
method Differentially private algorithm with nearly-linear time complexity and optimal approximation factor.
result Achieves optimal approximation factor of 3 with modest sample complexity increase.
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its par…
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…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with dimension-independent error guarantees for several families of structured distributions…
Two log-linear approximations speed up optimal transport for deep learning applications.
problem Computing optimal transport in high dimensions is computationally expensive.
method Locality-sensitive hashing (LSH) and Nyström approximation with LSH-based sparse corrections.
result Log-linear time algorithms for entropy-regularized OT perform well in high-dimensional spaces.
This paper analyzes error in SKI for Gaussian Processes, providing conditions for linear time inference.
problem Lack of rigorous theoretical error analysis for SKI.
method Proved error bounds for SKI Gram matrix, examined error effects, provided practical guidelines.
result Identified two dimensionality regimes for SKI's scalability-accuracy trade-offs.
Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.
problem Calibrating estimations to improve performance with monotone transforms.
method Proposed linear-time and space algorithm for finding optimal monotone transforms for specific loss functions. Also proposed an anytime algorithm with linear space and pseudo-linearithmic time complexity.
result Optimal monotone transforms are unique and can be found efficiently for various strictly convex loss functions.
Bayesian optimization sped up to linear time.
problem Expensive function evaluations and cubic computational complexity.
method Flexible binary partitioning of the search space.
result Linear computational complexity and superior optimization performance.
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.
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-approximate UOT solutions. SCORE technique reduces BO's high-dimensional search costs.
problem Bayesian optimization's high computational costs in high-dimensional spaces.
method 1D reparametrization trick to maintain linear time complexity.
result Successfully finds global minimum in high-dimensional optimization.
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.
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.
Faster GW alignment for incomparable point clouds via low-rank couplings.
problem Aligning points across incomparable point clouds.
method Low-rank couplings and costs to solve Gromov-Wasserstein framework in linear time.
result Linear-time computation of Gromov-Wasserstein distances.
Linear time algorithm for random walk kernels on sparse graphs.
problem Efficient computation of general random walk kernels for large graphs.
method Sample dependent random walks to compute graph embeddings without direct graph product.
result Up to 27x faster and scalable to 128x larger graphs than previous methods.
Fast algorithm solves BVPs in linear time with probabilistic uncertainty.
problem Solving boundary value problems efficiently and accurately.
method Gauss--Markov prior tailored to BVPs, linear-time computation.
result Probabilistic solution with linear time complexity and comparable quality.
Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional nature of transition dynamics performing inference in the iHMM is difficult. In th…
COSMIC identifies LTV systems from large data sets efficiently.
problem Identification of discrete-time linear time-variant systems from large-scale data.
method Formulates as regularized least squares problem, develops closed-form algorithm with linear complexity.
result Achieves optimal results even with large data volumes, significantly faster than general solvers.
Algorithm solves word problem in mapping class group quickly.
problem Word problem in mapping class group of a surface.
method Quasi-linear time algorithm (O(n log^3(n))).
result Solves word problem efficiently.
Fast algorithms developed for adaptive and fully adaptive submodular maximization problems.
problem Maximizing submodular functions subject to constraints in linear time.
method Developed linear-time algorithms for two submodular maximization problems: adaptive and fully adaptive.
result Achieved (1−1/e−ε) approximation ratio for adaptive submodular maximization and $ rac{1-1/e-ε}{4-2/e-2ε}$ for fully adaptive submodular maximization. This work improves Gaussian process model selection for large datasets.
problem Prohibitively high computational cost in Gaussian process model selection.
method Linear-time scaling and computational uncertainty tradeoff.
result Computation-aware Gaussian processes can be trained on large datasets efficiently.
New algorithm clusters data with almost-linear time, robust to corruption.
problem Clustering mixtures of distributions with adversarial corruption.
method List-decodable mean estimation, robust mean estimation, iterative multi-filtering.
result First almost-linear time algorithms for clustering mixtures of k well-behaved distributions.
SURF simplifies distribution estimation with simple, robust, and fast algorithms.
problem Efficient and accurate distribution estimation in statistics and machine learning.
method Piecewise polynomial approximation using empirical probability interpolation and divide-and-conquer merging.
result Surpassing state-of-the-art algorithms in efficiency and accuracy, SURF estimates distributions robustly and quickly.
CIfly simplifies causal inference tasks with linear-time reachability primitives.
problem Efficiently solving complex causal inference problems.
method Formalizes reachability as a core operation, builds on state-space graphs, and uses rule tables.
result CIfly algorithms run in linear time, outperforming existing methods.
New method robust to semi-random sparse recovery, nearly-linear time.
problem Brittleness of fast sparse recovery algorithms under generative model changes.
method Designing a new iterative method robust to semi-random model.
result Proves robustness of new method to semi-random generative models.
New algorithm maximizes non-monotone adaptive submodular functions in linear time.
problem Maximizing non-monotone adaptive submodular functions subject to a cardinality constraint.
method Developed a linear-time algorithm for non-monotone adaptive submodular maximization.
result Achieved a 1/e−ε approximation ratio with O(nε−2logε−1) value oracle queries. We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer…
McKernel introduces a framework to use kernel approximates in the mini-batch setting with Stochastic Gradient Descent (SGD) as an alternative to Deep Learning. Based on Random Kitchen Sinks [Rahimi and Recht 2007], we provide a C++ library for Large-scale Machine Learning. It contains a CPU optimized implementation of …
A new method for steering large agent populations efficiently.
problem Controlling the configuration of a swarm of identical, interacting cooperative agents.
method Mean-Field Schrodinger Bridges with Gaussian Mixture Models.
result A highly efficient parameterization to approximate optimal solutions of the MFSB problem in closed form.
Novel algorithm reduces privacy noise in machine learning.
problem High privacy noise in machine learning algorithms.
method Robust statistics, specifically median and trimmed mean, to bound sensitivity of SGD iterates.
result Improved privacy-utility trade-off with reduced noise and computational efficiency.