Study on maximizing submodular functions with limited updates, achieving tight bounds and poly-time algorithms.
problem Online submodular maximization with constant recourse.
method Information-theoretic bounds and poly-time randomized algorithms.
result Achieved tight bounds of 2/3 and 3/4 for general and coverage functions, respectively, with a 0.51 approximation.
This paper explores the limits of deep learning in poly-time.
problem Characterizing function distributions that deep learning can or cannot learn efficiently.
method Analysis of SGD and GD-based deep learning approaches, proving universality and non-universality results.
result SGD-based deep learning is efficiently universal, while GD-based is not, especially with large batches.
New algorithm learns random neural networks efficiently.
problem Learning random constant-depth neural networks efficiently.
method Presented a PTAS (Polynomial-Time Approximation Scheme) for learning random Xavier networks of fixed depth.
result For any fixed ε and depth i, there is a poly-time algorithm that learns random Xavier networks up to an additive error of ε.
New computational lower bounds for clustering and related problems.
problem Statistical-computational gaps in high-dimensional clustering problems.
method Investigation of low-degree polynomials in latent space models to derive lower bounds.
result New and sharper computational lower bounds for clustering, sparse clustering, and biclustering.
Simpler algorithm learns shallow networks faster.
problem Learning a linear combination of ReLU activations.
method A simpler one-stage algorithm with improved runtime.
result Runs in (d/ε)O(k2) time. The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency is measured by optimality criteria, including A(verage), D(eterminant), T(race)…
The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability, graph structured anomaly detection serves as a case study in the difficulty of bal…
New algorithm B++&C improves hierarchical clustering on large deep embedding datasets.
problem Scaling up hierarchical clustering to massive datasets of deep embeddings.
method Proposes B++&C algorithm for practical hierarchical clustering, introduces B2SAT&C for theoretical approximation.
result Achieves 5%/20% improvement on MW/CKMM objectives compared to classic methods.
Polynomial delay algorithm tests causal models with hidden variables.
problem Testing causal models with hidden variables in polynomial delay.
method c-component local Markov property (C-LMP) and polynomial delay algorithm.
result First algorithm for poly-delay testing of CIs in causal graphs with hidden variables.
The paper studies continuous submodular functions and their optimization.
problem Maximizing continuous submodular functions in poly. time.
method Characterization of continuous submodularity, operations preserving it, and algorithms for constrained maximization.
result Continuous submodularity is equivalent to a weak DR property, leading to continuous DR-submodular functions with the full DR property.
Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there are many other applications in which only \emph{multi}-way similarity measures ar…
We consider the problem of learning the weighted edges of a graph by observing the noisy times of infection for multiple epidemic cascades on this graph. Past work has considered this problem when the cascade information, i.e., infection times, are known exactly. Though the noisy setting is well motivated by many epide…
Algorithm clusters mixtures with bounded covariances under specific separation conditions.
problem Clustering mixtures of bounded covariance distributions with fine-grained separation.
method Introduced clustering refinement and efficient algorithm for accurate clustering.
result First poly-time algorithm for nearly uniform mixtures, and efficient refinement for general mixtures.