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.
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.
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. 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.
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.
Polynomial-time algorithm learns causal graphs without parametric assumptions.
problem Learning causal graphs from data without assuming linearity or parametric forms.
method Model-free polynomial-time algorithm with finite-sample guarantees.
result Algorithm achieves linear cost in dimension and samples compared to optimal.
Continuous-time algorithms improve online learning performance.
problem Online learning with sequential data and minimizing overall regret.
method Extending discrete-time algorithms to continuous-time models for online linear optimization, adversarial bandit, and adversarial linear bandit.
result Optimal regret bounds are proven for continuous-time settings.
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work shows that the eigenspectrum of unknown linear dynamics can be identified without…
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.
Robust learning mixtures of linear regressions improve robustness.
problem Improving robustness in learning mixtures of linear regressions.
method Connecting mixtures of linear regressions and mixtures of Gaussians with thresholding for a quasi-polynomial time algorithm.
result The algorithm has significantly better robustness than previous results.
New algorithms explain Naive Bayes classifiers in polynomial time and delay.
problem Computing explanations for Naive Bayes classifiers efficiently.
method Developed log-linear time and polynomial delay algorithms for PI-explanations.
result Efficiently computed PI-explanations for linear classifiers.
Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.
problem Optimizing control actions in unknown continuous-time systems over a finite time horizon.
method Least-squares algorithm based on continuous-time observations and controls, with perturbation analysis and parameter estimation error analysis.
result Logarithmic regret bound of order O((lnM)(lnlnM)). 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).
Classic contextual bandit algorithms for linear models, such as LinUCB, assume that the reward distribution for an arm is modeled by a stationary linear regression. When the linear regression model is non-stationary over time, the regret of LinUCB can scale linearly with time. In this paper, we propose a novel multisca…
Polynomial-time RL algorithm for constant actions under linear Bellman completeness.
problem Efficient online reinforcement learning with few actions.
method Polynomial-time algorithm based on linear function approximation.
result First computationally efficient algorithm for RL with constant actions under linear Bellman completeness.
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. Unified framework for integrating linear constraints in time series forecasting.
problem Challenges in traditional time series forecasting algorithms.
method Unified framework combining linear constraints in time series forecasting.
result Exact minimizer of the constrained empirical risk can be computed efficiently using linear algebra.
New algorithms solve dense linear systems with low-rank structure efficiently.
problem Solving dense linear systems with specific singular value conditions.
method Randomized algorithms using matrix sketching and low-rank update formulas.
result Achieves nearly-linear time complexity for solving such systems.
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.
New algorithms solve linear bandits in high dimensions efficiently.
problem Maximizing bilinear functions over convex sets and ellipsoids.
method Two novel algorithms for solving the problem efficiently.
result First known method to implement optimistic algorithms for linear bandits in high dimensions.
Faster algorithms for structured SVMs reduce computation time.
problem Efficiently solving quadratic programming problems with specific structures.
method Designing nearly-linear time algorithms for quadratic programs with low-rank factorizations and few linear constraints.
result First nearly-linear time algorithms for solving quadratic programs with specific structures.
Improved SVRG for quadratic functions achieves better performance and running times.
problem Minimizing quadratic functions with a specific type of Hessian matrix.
method Variant of SVRG algorithm for quadratic functions with improved analysis.
result Improved performance and running times for quadratic functions compared to state-of-the-art 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.
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.
New algorithm learns linear dynamical systems from measurements.
problem Learning system dynamics from linear measurements efficiently and accurately.
method Method of moments estimator to directly estimate Markov parameters.
result First polynomial time algorithm for learning linear dynamical systems.
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.
PILOT is a fast algorithm for linear model trees that outperforms existing methods.
problem Fitting linear model trees to large datasets efficiently and accurately.
method Greedy training with L2 boosting and model selection rule. result PILOT outperforms standard decision trees and other linear model trees on various datasets.
New algorithm learns Bayesian networks robustly in nearly-linear time.
problem Learning Bayesian networks with adversarially corrupted samples.
method Developed a nearly-linear time algorithm connecting robust learning to robust mean estimation.
result First nearly-linear time algorithm with comparable error 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.
Paper models non-linear dynamics from time series data.
problem Modeling non-linear dynamical systems from time series data.
method Introduces latent state modeling and a novel alternating minimization algorithm.
result LaNoLem achieves competitive performance in dynamics estimation and prediction.
Safety is a desirable property that can immensely increase the applicability of learning algorithms in real-world decision-making problems. It is much easier for a company to deploy an algorithm that is safe, i.e., guaranteed to perform at least as well as a baseline. In this paper, we study the issue of safety in cont…
We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear separators. We consider both the malicious noise model and the adversarial label nois…
Develops efficient algorithms for learning latent-variable models using implicit moment tensor computation.
problem Learning latent-variable models with moment tensors of super-constant degree.
method Implicit moment tensor computation for general models, extending previous work on clustering mixtures of spherical Gaussians.
result First poly(d, k) time learning algorithms for various models including mixtures of linear regressions, spherical Gaussians, and positive linear combinations of non-linear activations.
Theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
problem Lack of precise theoretical justification for asymmetric actor-critic algorithms in reinforcement learning.
method Adapting a finite-time convergence analysis to the asymmetric actor-critic setting with linear function approximators.
result A finite-time bound reveals that the asymmetric critic eliminates aliasing errors in the agent state.
Improved algorithm for conditional linear regression with heterogeneous covariances.
problem Identifying a linear predictor for a fraction of data with varying covariances.
method Polynomial time algorithm using Disjunctive Normal Form (DNF) to identify a condition and linear predictor.
result Removed requirement for similar covariances in each condition term, improving algorithm applicability.
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.
LLT transforms time series features based on linear laws.
problem Classifying univariate and multivariate time series.
method Time-delay embedding, spectral decomposition, and feature transformation.
result Transformed features improve classification accuracy.
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…
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.
Many real-world problems like Social Influence Maximization face the dilemma of choosing the best K out of N options at a given time instant. This setup can be modeled as a combinatorial bandit which chooses K out of N arms at each time, with an aim to achieve an efficient trade-off between exploration and expl…
Inference-aware meta-alignment of LLMs reduces computational cost.
problem Aligning LLMs to diverse human preferences is challenging due to conflicting criteria.
method IAMA trains a base model to be aligned to multiple tasks via different inference-time alignment algorithms, using non-linear GRPO for optimization.
result IAMA enables effective alignment of LLMs to multiple criteria with limited computational budget.
Study online control of unknown time-varying systems with negative and positive results.
problem Online control of time-varying systems with unknown dynamics.
method Algorithmic upper bounds and lower bounds for different policy classes.
result Sublinear adaptive regret bounds for Disturbance Response policies.
Paper tackles online facility location with user requests and provides a quasi-linear time algorithm.
problem Online facility location problem with user requests and site selection costs.
method Design of a novel quasi-linear time algorithm based on the Hedge algorithm.
result Good theoretical guarantees on the performance of the novel algorithm.
DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are linear in the number of time-series, they are generally quadratic in time-series l…
Solves steering problem with continuous time, Hilbert-Schmidt cost, and matrix ODEs.
problem Fixed horizon linear quadratic covariance steering in continuous time with a specific terminal cost.
method Formulates necessary conditions as a coupled matrix ODE two-point boundary value problem, designs a matricial recursive algorithm, and proves convergence.
result Proposes and proves the convergence of a matricial recursive algorithm for solving the steering problem.
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…
New algorithm tests model calibration in nearly-linear time.
problem Testing model calibration from samples efficiently.
method Reformulated as minimum-cost flow, solved with dynamic programming.
result Optimal testing problem solved in nearly-linear time.
New approach learns mixtures of linear dynamical systems without separation conditions.
problem Learning mixtures of linear dynamical systems with better fit or understanding.
method Tensor decompositions to learn mixtures of linear dynamical systems.
result Algorithm succeeds without strong separation conditions and can compete with Bayes optimal clustering.