Investigates polynomial time algorithms for computing Khovanov homology of braids.
problem Computing Khovanov homology for general braids is intractable.
method Examines polynomial time algorithms for 3-braids and a variation of the scanning algorithm for more general braids.
result Shows that for 3-braids, Khovanov homology can be computed in polynomial time, while for more general braids, it can be computed in polynomial time for bounded homological degrees.
Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.
problem Matching vertices in two correlated Erdős-Rényi graphs.
method Iterative matching algorithm for correlated Gaussian Wigner matrices.
result First polynomial time algorithm for graph matching with arbitrarily small constant correlation.
Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.
problem Matching correlated random graphs with non-vanishing edge correlation.
method Iterative algorithm for polynomial-time recovery of latent matching.
result Algorithm succeeds in recovering latent matching as long as edge correlation is non-vanishing.
Algorithm classifies surface homeomorphisms with polynomial time complexity.
problem Classifying surface homeomorphisms with polynomial time complexity.
method Algorithm to compute curve distances and decide Nielsen-Thurston types.
result Polynomial time classification of surface homeomorphisms.
Polynomial-time methods count and sample DAGs from equivalence classes.
problem Counting and sampling DAGs from Markov equivalence classes.
method Polynomial-time algorithms for DAGs.
result Counting and sampling can be done in polynomial time.
Strongly polynomial algorithm for approximate Forster transforms and halfspace learning.
problem Computing approximate Forster transforms and halfspace learning.
method Strongly polynomial time algorithm for approximate Forster transforms and halfspace learning.
result First strongly polynomial time algorithm for distribution-free PAC learning of halfspaces.
EKM solves the K-medoids problem in polynomial time.
problem The K-medoids problem in data analysis. method EKM is a novel algorithm using transformational programming and combinatorial generation.
result EKM solves the K-medoids problem in worst-case $O\left(N^{K+1}
ight)$ time complexity. Algorithm learns halfspaces with Tsybakov noise in polynomial time.
problem PAC learning halfspaces with adversarial noise.
method Reduction to certifying non-optimality, iterative process, warm-start algorithm.
result First polynomial-time algorithm for learning halfspaces with Tsybakov noise.
Polynomial-time algorithm for near-optimal community detection in graphs.
problem Node-private community estimation in stochastic block models.
method Explicit Lipschitz surrogate and accept-reject algorithm for sampling community labels.
result Achieves minimax rates for exact recovery with polynomial-time runtime and logarithmic privacy parameter.
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.
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.
In this paper we study the adaptive learnability of decision trees of depth at most d from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman solves the problem in a randomized polynomial time algorithm that asks $\tilde O(2^…
New algorithm speeds up polynomial kernel approximations.
problem Efficiently approximating polynomial kernels of high degree.
method Oblivious sketching combined with novel sampling.
result Polynomial factor slowdown removed in running time.
New algorithm learns decision trees faster than before.
problem Properly learning decision trees in polynomial time.
method Membership query algorithm with nO(loglogn) time complexity. result Achieved faster learning time for decision trees.
New algorithm recovers sparse measures in polynomial time.
problem Recovering sparse measures from Fourier moments.
method Polynomial-time recovery method inspired by mean-field theory.
result Improves upon convex relaxation methods in specific parameter regime.
Polynomial-time algorithm estimates mean with bounded covariance using differential privacy.
problem Estimating mean of a d-variate distribution with differential privacy constraints.
method Sum of Squares (SoS) exponential mechanism for polynomial-time differentially private estimation.
result First polynomial-time algorithm with O(d) samples for mean estimation under pure differential privacy. New algorithm speeds up knot polynomial calculations.
problem Computing Reshetikhin--Turaev knot polynomials efficiently.
method Fixed-parameter tractable computation via tensor networks.
result Knot polynomial computations are fixed-parameter tractable.
Polynomial-time DP algorithm for learning Gaussians with matching sample complexity.
problem Learning Gaussian distributions while maintaining privacy.
method General framework for reducing DP estimation to non-private, polynomial-time algorithm for Gaussian learning.
result Matching sample complexity to information-theoretic upper bound for Gaussian learning.
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.
We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves, this has several applications to mapping classes. For example, we can use these geodesics to compute the asymptotic translation length, Ni…
Polynomial-time algorithm learns high-dimensional halfspaces without labels.
problem Learning high-dimensional halfspaces with margins in polynomial time.
method Contrastive moments and polynomial-time algorithm.
result Establishes the unique and efficient identifiability of the hidden halfspace.
Algorithm creates polynomials for knotted surfaces, with bounds on degree.
problem Creating polynomials for knotted surfaces with constraints.
method Algorithm constructs polynomials based on loop braids and surface braids.
result Upper bounds on the degree of polynomials for knotted surfaces.
Polynomial-time method solves complex combinatorial semi-bandits.
problem Optimal strategies for combinatorial semi-bandits with uncorrelated Gaussian rewards.
method Proposes a polynomial-time method to solve the Graves-Lai optimization problem for various combinatorial structures.
result First known approach to implement asymptotically optimal algorithms in polynomial time for combinatorial semi-bandits.
We show that the standard stochastic gradient decent (SGD) algorithm is guaranteed to learn, in polynomial time, a function that is competitive with the best function in the conjugate kernel space of the network, as defined in Daniely, Frostig and Singer. The result holds for log-depth networks from a rich family of ar…
Polynomial-time methods count and sample DAGs from Markov classes.
problem Counting and sampling Markov equivalent DAGs.
method Polynomial-time algorithms for DAGs from Markov classes.
result Long-standing open problem solved, making practical infeasible strategies feasible.
Polynomial-time algorithm for clustering mixtures with separation Δ=Ω(√(log k)).
problem Clustering mixtures of mean-separated Gaussians in high dimensions.
method Polynomial-time algorithm using implicit moment estimation.
result Achieves almost optimal clustering guarantee with separation Δ=Ω(√(log k)).
Abstract reviews algorithms for multi-index models, focusing on polynomial-time methods and their limitations.
problem Estimating the index space in multi-index models efficiently and accurately.
method Polynomial-time algorithms in Gaussian space, nonparametric gradient estimation, and neural network fitting.
result A gap exists between computationally efficient methods and information-theoretical minimum.
Sparse PCA algorithm improves upon existing methods with better guarantees.
problem Recovering sparse vectors from Gaussian samples with adversarial perturbations.
method New algorithm running in polynomial time with improved β threshold.
result Better guarantees than Covariance Thresholding for large t.
New algorithms improve approximation of matrix norms, with applications in statistics and machine learning.
problem Improving approximation of matrix norms for 2ightarrowq in polynomial time. method Polynomial-time multiplicative approximation algorithms for 2ightarrowq norm, leveraging sum-of-squares certificates. result Achieved polynomially improved approximation factors, notably d1/8 for q=4. Algorithm distinguishes Gaussian mixtures from pure Gaussians in quasi-polynomial time.
problem Distinguishing mixtures of Gaussian components from pure Gaussians, especially when components are well-separated.
method Sum-of-Squares method, quasi-polynomial time algorithm, bipartitioning sample to separate components.
result Algorithm can reliably distinguish between mixtures and pure Gaussians in quasi-polynomial time.
Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning. We present SURF, an algorithm for approximating distributions by piecewise polynomials. SURF is: simple, replacing prior complex optimization techniques by straight-forward {empirical probability} ap…
We describe the polynomial time complexity algorithm for computing first coefficients of the skein (Homflypt) and Kauffman polynomial invariants of links, discovered by D.Vertigan in 1992 but never published.
Polynomial-time algorithm solves random parity games with high probability.
problem Solving random parity games efficiently.
method SWCP algorithm based on cycles in subgraphs.
result Polynomial-time solution for large-degree games with high probability.
Algorithm learns polynomial transformations of Gaussian distributions.
problem Learning high-dimensional polynomial transformations of Gaussian distributions.
method Polynomial-time algorithms for smoothed settings, tensor ring decomposition.
result First end-to-end guarantees for learning pushforwards under neural networks.
Low-degree method fails to predict robust subspace recovery problem.
problem Predicting computational tractability of robust subspace recovery problem.
method Low-degree polynomial framework, anti-concentration properties.
result Low-degree method fails to predict computational tractability of robust subspace recovery problem even up to high degree.
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics, making them especially challenging. Standard approaches, often relying on ADP, dualit…
The colored Jones polynomial is a knot invariant that plays a central role in low dimensional topology. We give a simple and an efficient algorithm to compute the colored Jones polynomial of any knot. Our algorithm utilizes the walks along a braid model of the colored Jones polynomial that was refined by Armond from th…
New algorithm optimizes matrix reordering for noisy disordered matrices.
problem Optimizing matrix reordering for noisy disordered matrices in single-cell biology and metagenomics.
method Proposed a polynomial-time adaptive sorting algorithm to improve upon spectral seriation.
result Our algorithm achieves superior performance compared to existing methods in real datasets.
Polynomial-time algorithm learns ReLU networks without assumptions.
problem Learning linear combinations of ReLU activations with Gaussian inputs.
method Random contractions of moment tensors and multi-scale analysis.
result First polynomial-time algorithm without additional assumptions.
New algorithm speeds up learning of graphical models.
problem Learning graphical models with sparse structure efficiently.
method Vertex-greedy score-based algorithm for learning DAGs.
result Polynomial runtime for learning DAG models.
Parallel algorithm speeds up Jones polynomial computation.
problem Efficient computation of knot complexity measures.
method First parallel algorithm for exact Jones polynomial computation.
result Reduces computational time by an exponential factor.
Polynomial-time algorithm for estimating covariance in corrupted Gaussian data.
problem Estimating covariance in data with up to 1-α fraction of adversarial corruptions.
method Uses low-degree sum-of-squares certificates for anti-concentration and hypercontractivity.
result Outputs a list of candidate parameters with high probability containing a nearly correct covariance.
We propose an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in the word-length of an input braid. Moreover, a reduction system of circles can be found completely if the input is a certain type of r…
MAP perturbation models have emerged as a powerful framework for inference in structured prediction. Such models provide a way to efficiently sample from the Gibbs distribution and facilitate predictions that are robust to random noise. In this paper, we propose a provably polynomial time randomized algorithm for learn…
Polynomial-time algorithm for learning halfspaces with Gaussian-distributed data and adversarial noise.
problem Learning halfspaces in the presence of adversarial label noise.
method Iterative soft localization technique enhanced with appropriate testers.
result Output a halfspace with misclassification error $O(\opt)+\eps$.
Polynomial-time algorithm for list-decodable linear regression with batches.
problem Efficiently decoding linear regression with a fraction of adversarial data.
method Polynomial time algorithm using batches of i.i.d. samples.
result Returns a list of size O(1/α^2) with one item close to true parameter.
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…
Paper extends Cohen's method to compute Jones polynomial for certain braid subfamilies.
problem Computing Jones polynomial for specific knot families.
method Using weighted adjacency matrices and determinants for certain subfamilies of braid groups.
result Jones polynomial can be computed in polynomial time for certain subfamilies of braid groups.