Modified K-means ensures local optimality with same complexity.
problem Lack of rigorous analysis on local optimality guarantees of K-means.
method Proposed modifications to K-means ensuring local optimality.
result Proposed methods provide improved locally optimal solutions.
Proposes a new algorithm to find local Nash equilibria in zero-sum games.
problem Cannot guarantee convergence to local Nash equilibria with previous methods.
method Local symplectic surgery, a two-timescale procedure.
result Local Nash equilibria are the only attracting fixed points.
LocalKMeans parallelizes Lloyd's algorithm for distributed data.
problem Efficiently clustering data across multiple machines.
method Parallel local iterations with synchronization every L steps.
result Higher required signal-to-noise ratio due to local steps.
MPHL algorithm improves wireless network localization using distance and direction data.
problem Accurate and affordable positioning in wireless networks.
method Hybrid approach combining distance and direction estimates, statistical model, belief propagation, and MCMC sampling.
result Significant reduction in localization error, up to 50% compared to competing algorithms.
New algorithms adaptively compete against complex environments with local regularities.
problem Efficiently competing against complex, locally regular comparator functions in nonparametric settings.
method Locally-adaptive online algorithms using hierarchical ε-nets and tree experts. result Proved regret bounds scaling with different types of local regularities, delivering better performance for simple profiles.
Faster algorithm finds approximate local minima.
problem Finding approximate local minima in non-convex optimization problems.
method Non-convex second-order optimization algorithm.
result Finds approximate local minima faster than gradient descent.
Unified framework for combinatorial and rounding algorithms in experimental design.
problem Designing and analyzing combinatorial and rounding algorithms for experimental design problems.
method Local search framework for combinatorial algorithms and regret minimization framework for rounding algorithms.
result Unified approach to match and improve all known results in D/A/E-design and obtain new results in unknown settings.
There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed t…
This paper analyzes saddle points and minimax points in non-convex smooth games.
problem Understanding local optimal points in non-convex smooth games.
method Comprehensive analysis of local minimax points, including their optimality conditions and stability.
result Local saddle points are uniformly local minimax points under mild continuity assumptions.
New locally private algorithm for k-means clustering reduces additive error significantly.
problem Designing a locally private algorithm for k-means clustering with reduced additive error.
method Local differential privacy approach, reducing additive error to nearly n1/2. result Achieves O(1) multiplicative error and n1/2+a additive error, nearly optimal. This paper introduces a scalable benchmark for evaluating local posterior sampling in neural networks.
problem Degeneracy in neural network loss landscapes and its impact on SGMCMC algorithms.
method Development of a scalable benchmark for local posterior sampling.
result RMSProp-preconditioned SGLD is most effective at representing the local geometry of the posterior distribution.
Paper tackles indoor localization issues with reduced dimensionality and improved fingerprint matching.
problem Curse of dimensionality and asymmetric matching in fingerprint-based indoor localization.
method Proposes a semi-supervised RSS dimensionality reduction algorithm and integrates it with a fingerprint-based algorithm.
result Improves indoor localization accuracy by reducing dimensionality and addressing matching issues.
A study compares local music recommendation algorithms, finding neighborhood-based methods perform best.
problem Cold-start problem for local artists with little user preference data.
method Comparison of three recommender system algorithms (IIN, ALS, BPR) on local music recommendation task.
result Neighborhood-based approach (IIN) performs best for local music recommendation.
Localized inference for large graphs with error bounds.
problem Efficiently answering queries in large graphical models.
method Localized algorithm with error bounds based on Dobrushin's theorem.
result Localized inference provides fast and accurate approximations for large models.
Local algorithms perform well on SDP relaxations of graph bisection problems.
problem Understanding the performance of local algorithms on SDP relaxations of graph bisection problems.
method Used dual witness construction and harmonic measure on limiting Galton-Watson tree.
result Simple local algorithms are at most 8/9 suboptimal for graph bisection problems.
Reduces non-convex optimization to finding local minima using gradients.
problem Finding local minima in non-convex optimization problems.
method Reduces non-convex optimization to gradient-based methods.
result Turns various optimization algorithms into local minimum finding methods.
Proximal splitting methods solve rank-constrained convex problems locally.
problem Solving optimization problems with rank constraints.
method Proximal splitting algorithms with conditions on rank constraint convex envelopes.
result Proximal splitting methods converge locally to solutions under convex relaxation conditions.
FALL improves local model training with anchor regularization.
problem Efficient local model training in regression tasks.
method Regularization with precomputed anchor models, closed-form solution.
result FALL outperforms network Lasso in accuracy with significantly less training time.
Proves local convergence of various online and recurrent optimization algorithms.
problem Proves local convergence of online and recurrent optimization algorithms not covered by standard stochastic gradient descent theory.
method Uses a general set of assumptions for learning dynamical systems online, adopting an 'ergodic' viewpoint.
result Local convergence results for online and recurrent optimization algorithms, including RMSProp, NoBackTrack, UORO, Adam, and RTRL.
Local search algorithms applied to optimization problems often suffer from getting trapped in a local optimum. The common solution for this deficiency is to restart the algorithm when no progress is observed. Alternatively, one can start multiple instances of a local search algorithm, and allocate computational resourc…
Locally private reinforcement learning protects individual environments from reverse engineering.
problem Protecting private information in distributed reinforcement learning environments.
method Locally differentially private algorithms that protect local agents' models from adversarial reverse engineering.
result Demonstrated that the proposed algorithm performs well under local differential privacy (LDP).
Novel algorithm estimates local permutations in unlabeled multi-view sensing.
problem Estimating local permutations in unlabeled multi-view sensing.
method Graph alignment and Gromov-Wasserstein alignment exploiting multiple views.
result The proposed algorithm is scalable and applicable to challenging SNR regimes.
PL-NMF improves parallel NMF by optimizing data locality.
problem Data movement costs dominate in parallel NMF applications.
method Developed a parallel NMF algorithm based on HALS with data locality optimizations.
result Significant performance improvement over existing parallel NMF algorithms.
Overlap-Local-SGD improves distributed SGD by overlapping communication and computation.
problem High communication delay and node slowdown in distributed SGD.
method Adding an anchor model to synchronize local updates and pull them towards the anchor model.
result Overlap-Local-SGD speeds up distributed training and mitigates straggler effects.
PGD algorithm converges to local minima in nonconvex matrix completion.
problem Matrix completion with low-rank promotion using nonconvex penalties.
method Proximal gradient descent algorithm for nonconvex penalties.
result PGD algorithm converges to restricted strictly local minimizers with eventually linear rate.
Locally private Gaussian estimation tackles privacy in i.i.d. sample mean estimation.
problem Estimating the mean of an unknown Gaussian distribution while maintaining local differential privacy for each user.
method Adaptive two-round and nonadaptive one-round solutions for locally private Gaussian estimation.
result Upper bounds partially match with information-theoretic lower bounds, showing tightness up to logarithmic factors.
Unified analysis of efficient local training methods for distributed variational inequalities.
problem Efficient distributed/federated learning for variational inequality problems.
method Unified convergence analysis of communication-efficient local training methods.
result First local gradient descent-accent algorithms with improved communication complexity.
Improved algorithm for selecting a hypothesis locally privately with fewer queries.
problem Locally private hypothesis selection with minimal privacy-preserving queries.
method Introduces a Scheffé graph to reduce query complexity for hypothesis selection.
result Algorithm performs O~(k3/2) queries, improving on previous methods. New Q-Learning algorithm reduces switching cost in MDPs.
problem Reducing adaptivity in real-world applications.
method Q-Learning with UCB2 exploration, quantified by local switching cost.
result Achieves sublinear regret with low switching cost.
Learning a Bayesian network structure from data is an NP-hard problem and thus exact algorithms are feasible only for small data sets. Therefore, network structures for larger networks are usually learned with various heuristics. Another approach to scaling up the structure learning is local learning. In local learning…
Paper proposes FR algorithm to solve minimax optimization locally.
problem Gradient descent fails to find local minimax in minimax optimization.
method Follow-the-Ridge (FR) algorithm, addressing rotational behavior of gradient dynamics.
result FR algorithm provably converges to local minimax.
New method calibrates local volatility models to marginal distributions.
problem Calibrating local volatility models to specific marginal distributions.
method Inspired by volatility interpolation, constructs time-homogeneous or continuous local volatility functions.
result Efficient numerical algorithms for constructing local volatility functions.
This paper analyzes a simplified strategy for nonlinear control using local linear models and iLQR updates.
problem Nonlinear policy optimization in control systems.
method Iterative estimation of local linear models and iLQR-like policy updates.
result Demonstrates polynomial sample complexity and overcomes exponential problem horizon dependence.
New FL framework handles non-i.i.d data without strong assumptions.
problem Non-identically independent distributed (non-i.i.d) data in federated learning.
method Proposes a new algorithm design strategy from primal-dual optimization.
result Achieves optimal communication efficiency and communication complexity.
This paper enhances ML algorithms by improving data locality and reducing redundancy.
problem Improving performance of machine learning algorithms with complex data.
method Exploiting data locality and reuse in memory hierarchies of modern processors.
result Efficient implementation of machine learning algorithms can be achieved by reusing computation results.
HALO uses local Lipschitz constants to optimize functions efficiently.
problem Efficiently solving global optimization problems with complex objective functions.
method Hybrid Adaptive Lipschizian Optimization (HALO) algorithm that estimates local Lipschitz constants and balances global and local information.
result HALO outperforms other global optimization algorithms on numerous test functions.
Adversarial online nonparametric regression achieves optimal rates with locally adaptive learning.
problem Adversarial online nonparametric regression with general convex losses.
method Parameter-free learning algorithm leveraging chaining trees to compete against H{ö}lder functions, dynamically tracking and adapting to local smoothness variations.
result First computationally efficient algorithm with locally adaptive optimal rates for online regression in an adversarial setting.
A new algorithm optimizes local objectives in federated learning with heterogeneous clients.
problem Optimizing local objectives in federated learning with heterogeneous client data.
method Proposes PF-PNE algorithm with double elimination strategy.
result PF-PNE algorithm optimizes local objectives with arbitrary heterogeneity and protects client data confidentiality.
Reduces sound event localization error by 2.6x with hybrid parametric-deep learning.
problem Sound event localization and detection accuracy.
method Hybrid approach combining parametric spatial audio analysis and deep learning.
result Reduction of localization error by 2.6x compared to baseline.
Given a subset S of vertices of an undirected graph G, the cut-improvement problem asks us to find a subset S that is similar to A but has smaller conductance. A very elegant algorithm for this problem has been given by Andersen and Lang [AL08] and requires solving a small number of single-commodity maximum flow comput…
Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurem…
New local-search methods close the gap in sparse tensor PCA.
problem Sparse tensor PCA underperforms compared to other methods.
method Proposes new local-search methods including greedy and random-threshold variants.
result Proves local-search methods close the gap to best known polynomial-time procedures.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
The paper analyzes early stopping for boosting algorithms using localized Gaussian complexity.
problem Understanding the performance of early stopping in kernel boosting algorithms.
method Direct connection between stopped iterate performance and localized Gaussian complexity of function classes.
result Optimal stopping rules derived for various kernel classes, showing correspondence with practice.
New insights into spurious local minima in k-means clustering.
problem Understanding and mitigating spurious local minima in k-means clustering.
method Investigating spurious local minima under a probabilistic generative model.
result Proven structures of spurious local minima for k-means clustering.
Local network community detection is the task of finding a single community of nodes concentrated around few given seed nodes in a localized way. Conductance is a popular objective function used in many algorithms for local community detection. This paper studies a continuous relaxation of conductance. We show that con…
A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of 2 forms, to be skew symmetric with respect to some local frame. In this paper we give a simple algorithm that can be used to decide when a matrix of 2 forms is equivalent to a skew symmetric…
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of granularity to capture diverse types of local information for subsequent machine lea…