Study exact community recovery in noisy SBM with limited queries.
problem Community recovery in noisy stochastic block models with limited queries.
method Balanced uniform querying, two-stage adaptive strategy, sublinear queries, subsampled graph.
result Adaptive querying can improve exact recovery limits in noisy SBM.
New sublinear sketches improve ANN and KDE for massive data streams.
problem Efficiently approximate nearest neighbors and kernel density estimation in large datasets.
method Developed sublinear space and query time algorithms for ANN and A-KDE in streaming and sliding-window models.
result Achieved near-optimal trade-offs between memory size and approximation error for ANN.
This work addresses dynamic KDE data structures with robustness to adversarial queries.
problem Efficient KDE data structures for dynamic changing data distributions.
method Developed a theoretical framework for KDE data structures that support subquadratic space, sublinear updates, and adaptive queries.
result Theoretical framework and practical implementation of KDE data structures robust to adversarial queries.
We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size O(Nblog3N) in O(N(b+1)log3N) time, where b<1. This sketch can correctly report the nearest neighbors of any …
Sublinear algorithms detect cliques in graphs with high probability.
problem Detecting a planted clique in random graphs efficiently.
method Non-adaptive low-degree polynomial queries of adjacency matrix entries.
result Sublinear time detection is possible for a specific range of clique sizes.
New algorithms save computation in agnostic learning with membership queries.
problem Efficiently learning touchstone classes with membership queries.
method Designing agnostic learning algorithms for circuits with sublinear gates.
result Agnostic learning algorithms for circuits with sublinear gates achieve significant computational savings.
The paper provides an almost optimal learning and testing algorithm for sparse polynomials.
problem Learning and testing sparse multivariate polynomials efficiently.
method The paper presents an algorithm with sublinear query complexity in 1/ε and almost linear in s for learning and testing s-sparse polynomials. result The algorithm achieves almost optimal query complexity, making it the first of its kind.
BILBO optimizes bilevel problems without repeated lower-level optimizations.
problem Challenges in bilevel optimization, especially in noisy, constrained, and derivative-free settings.
method BILevel Bayesian Optimization (BILBO) that optimizes both levels simultaneously, using confidence-bounds and function query selection.
result Theoretical and empirical evidence of BILBO's effectiveness on various problems.
New algorithms reduce rejection sampling complexity for shape-constrained distributions.
problem Generating exact samples from shape-constrained distributions efficiently.
method Sublinear query complexity algorithms for rejection sampling.
result Sublinear complexity algorithms for sampling from shape-constrained distributions.
Quantum algorithms reduce clustering input size, achieving near-linear approximation.
problem Efficiently clustering large datasets in quantum computing.
method Quantum coresets for k-clustering with sublinear query complexity. result Achieves near-linear approximation for k-clustering with coresets. Most exact methods for k-nearest neighbour search suffer from the curse of dimensionality; that is, their query times exhibit exponential dependence on either the ambient or the intrinsic dimensionality. Dynamic Continuous Indexing (DCI) offers a promising way of circumventing the curse and successfully reduces the dep…
The pair-matching problem appears in many applications where one wants to discover good matches between pairs of entities or individuals. Formally, the set of individuals is represented by the nodes of a graph where the edges, unobserved at first, represent the good matches. The algorithm queries pairs of nodes and obs…
Locality sensitive hashing (LSH) is a powerful tool for sublinear-time approximate nearest neighbor search, and a variety of hashing schemes have been proposed for different dissimilarity measures. However, hash codes significantly depend on the dissimilarity, which prohibits users from adjusting the dissimilarity at q…
Algorithm achieves logarithmic regret with sublinear hints.
problem Online linear optimization with limited hints.
method Using logarithmic hints to improve regret from sqrt(T) to log(T).
result O(log T) regret with O(sqrt(T)) hints, and O(sqrt(T)) regret with o(sqrt(T)) hints.
Real-world networks such as social and communication networks are too large to be observed entirely. Such networks are often partially observed such that network size, network topology, and nodes of the original network are unknown. In this paper we formalize the Adaptive Graph Exploring problem. We assume that we are …
Study online RL with mismatched dynamics, achieving sublinear regret.
problem Exploration challenges in online RL with mismatched training and deployment dynamics.
method Introduce supremal visitation ratio, propose efficient algorithm with f-divergence. result Achieves sublinear regret in online RMDPs with optimal dependence on supremal visitation ratio and interaction episodes.
Differentially private data structures for estimating distances between strings.
problem Estimating distances between query strings and database strings while ensuring privacy.
method Proposes differentially private data structures for Hamming and edit distances using randomized response technique.
result Efficient data structures that provide accurate distance estimates with strong privacy guarantees.
Lower bounds show density estimation requires linear samples or query time.
problem Statistical-computational trade-offs in density estimation.
method Lower bound analysis on data structures.
result Lower bounds demonstrate statistical-computational trade-offs for density estimation.
In this paper, we consider the problem of learning an unknown graph via queries on groups of nodes, with the result indicating whether or not at least one edge is present among those nodes. While learning arbitrary graphs with n nodes and k edges is known to be hard in the sense of requiring $Ω( \min\{ k^2 \log n, …
Algorithm reduces regret in distributed kernel bandits with shared randomness.
problem Minimizing regret in collaborative function maximization.
method Uniform exploration at local agents and shared randomness with central server.
result Achieves optimal regret order with sublinear communication cost.
Active sampling algorithm for linear regression with various norms and improved query complexity.
problem Efficiently querying a few entries of a target vector for near optimal minimizers of linear regression.
method Lewis weight sampling and active sampling algorithms for different p norms. result Optimal query complexity for p∈(0,1), 1<p<2, and 2<p<∞. Transformer models improve query-document retrieval efficiency and accuracy.
problem Efficiently retrieve relevant documents from large corpora for query matching.
method Designed paragraph-level pre-training tasks to optimize embedding-based Transformer models.
result Transformer models significantly outperform BM-25 and non-Transformer embedding models.
The paper shows how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.
problem Understanding how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.
method Defining sublinear biLipschitz equivalence and Morse boundaries, proving invariance under SBEs, using sublinear rays.
result κ-Morse boundaries of proper geodesic metric spaces are invariant under suitable sublinear biLipschitz equivalences.
New algorithms achieve optimal regret in sliding window model with limited memory.
problem Experts problem in the sliding window model with limited information.
method 2 queries, polylog(nT) memory, exponential improvement on memory.
result Achieve optimal regret of sqrt(nW)polylog(nT) with 2 queries and polylog(nT) memory.
A new algorithm reduces memory usage for long token attention in streaming applications.
problem Memory inefficiency in computing attention for long documents.
method One-pass streaming algorithm using sublinear space storage.
result Super-efficient memory usage for long token attention.
We study the problem of efficient PAC active learning of homogeneous linear classifiers (halfspaces) in Rd, where the goal is to learn a halfspace with low error using as few label queries as possible. Under the extra assumption that there is a t-sparse halfspace that performs well on the data (t≪d)…
The k-Nearest Neighbor Search (k-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In these services, the client sends the query to the cloud server and receives the response in which case the query and response are revealed t…
Sublinear LSVI via LSH reduces runtime to sublinear in actions.
problem Efficiently estimating value functions in reinforcement learning with sublinear runtime.
method Formulated as approximate maximum inner product search, used LSH to solve with sublinear time complexity.
result Sublinear runtime while maintaining LSVI's regret.
The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric space. For example, the sublinear Higson corona of n-dimensional E…
New model for Knightian uncertainty with jumps.
problem Knightian uncertainty and non-linear jumps.
method Probabilistic construction of non-linear affine processes with jumps.
result Tractable model for Knightian uncertainty with sublinear expectations.
We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…
Efficient Maximum Inner Product Search (MIPS) is an important task that has a wide applicability in recommendation systems and classification with a large number of classes. Solutions based on locality-sensitive hashing (LSH) as well as tree-based solutions have been investigated in the recent literature, to perform ap…
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…
Optimistic search speeds up change point detection in large datasets.
problem Efficiently detecting change points in large-scale data with high computational demands.
method Adaptive logarithmic queries to reduce evaluation complexity.
result Asymptotic minimax optimality and fast localization rates for change point detection.
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …
The paper develops methods for time-varying constrained online convex optimization.
problem Time-varying loss and constraint functions in online convex optimization.
method Model-based augmented Lagrangian methods (MALM) for time-varying and delayed feedback.
result Sublinear regret and constraint violation for both time-varying and delayed feedback scenarios.
For α∈(1,2), we present a generalized central limit theorem for α-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, p…
New algorithms for constrained online optimization with memory and predictions.
problem Control of constrained dynamical systems and scheduling with reconfiguration budgets.
method Proposed algorithms achieving sublinear regret and constraint violation under time-varying constraints, both with and without predictions.
result First algorithms achieving sublinear regret and constraint violation in constrained online optimization with memory.
Memory-limited learning tackles adversarial bandits with reduced storage.
problem Adversarial bandit problem with limited memory storage.
method Hierarchical learning policy with sublinear memory requirement.
result Established sublinear regret bounds for weak and shifting regrets.
Sharp Liouville theorem for minimal graphs on manifolds with nonnegative Ricci curvature.
problem Characterizing smooth solutions to minimal hypersurface equations on manifolds with nonnegative Ricci curvature.
method Gradient estimate for minimal graphs over Σ with small linear growth of the negative parts of graphic functions via iteration. result Every smooth solution u to minimal hypersurface equation on Σ is a constant provided u has sublinear growth for its negative part. New method connects CAT(0) spaces to hyperbolic spaces.
problem Injecting sublinear Morse boundaries into Gromov boundaries.
method Developed curtain machinery to characterize sublinear Morse properties.
result Continuous injection of sublinear Morse boundaries into Gromov boundaries.
Study online learning in unknown Markov games with sublinear regret.
problem Online learning in unknown Markov games with unobservable opponents.
method Introduced an algorithm achieving sublinear regret against the minimax value.
result First sublinear regret bound for unknown Markov games, independent of action spaces size.
Derivative-free optimization has become an important technique used in machine learning for optimizing black-box models. To conduct updates without explicitly computing gradient, most current approaches iteratively sample a random search direction from Gaussian distribution and compute the estimated gradient along that…
We consider black box optimization of an unknown function in the nonparametric Gaussian process setting when the noise in the observed function values can be heavy tailed. This is in contrast to existing literature that typically assumes sub-Gaussian noise distributions for queries. Under the assumption that the unknow…
Open problem seeks an online learning algorithm for binary classification.
problem Existence of an online learning algorithm for binary classification with sublinear mistakes.
method Assumption of sequence allowing learning algorithm's existence.
result Specific condition determines sequence's learnability.
Efficiently trains large GMMs with millions to billions of parameters.
problem Training large Gaussian Mixture Models (GMMs) is computationally expensive.
method Derives a variational approximation integrated with mixtures of factor analyzers (MFAs) to reduce complexity.
result Sublinear scaling in training GMMs, achieving significant speed-ups.
Average signature of 2-bridge knots approximates sqrt(2c/π).
problem Estimating the average signature and 4-genus of 2-bridge knots.
method Developed a model for 2-bridge knot diagrams indexed by crossing number, and used it to derive upper bounds for the average 4-genus.
result Upper bound for the average 4-genus of a 2-bridge knot is 9.75c/log c.
Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function cha…