Related papers: Efficient Algorithms for Learning Monophonic Halfs…
We consider the following two algorithmic problems: given a graph $G$ and a subgraph $H\subseteq G$, decide whether $H$ is an isometric or a geodesically convex subgraph of $G$. It is relatively easy to see that the problems can be solved…
Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…
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…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be…
We study the problem of agnostically learning homogeneous halfspaces in the distribution-specific PAC model. For a broad family of structured distributions, including log-concave distributions, we show that non-convex SGD efficiently…
Attribute-efficient PAC learning of sparse halfspaces has been a fundamental problem in machine learning theory. In recent years, machine learning algorithms are faced with prevalent data corruptions or even malicious attacks. It is of…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
For the first time we provide a succinct pattern matching index for arbitrary graphs that can be built in polynomial time, which requires less space and answers queries more efficiently than the one in [SODA 2021]. We show that, given an…
We study the problem of {\em distribution-independent} PAC learning of halfspaces in the presence of Massart noise. Specifically, we are given a set of labeled examples $(\mathbf{x}, y)$ drawn from a distribution $\mathcal{D}$ on…
Inspired by recent work on learning with distribution shift, we give a general outlier removal algorithm called iterative polynomial filtering and show a number of striking applications for supervised learning with contamination: (1) We…
We study computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded factor size and bounded connectivity can be learned in polynomial time…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus…
Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…
We give a polynomial-time algorithm for detecting very long cycles in dense regular graphs. Specifically, we show that, given $\alpha \in (0,1)$, there exists a $c=c(\alpha)$ such that the following holds: there is a polynomial-time…
The learning complexity of special sets of vertices in graphs is studied in the model(s) of exact learning by (extended) equivalence and membership queries. Polynomial-time learning algorithms are described for vertex covers, independent…
In this paper, we study the exact learning problem for weighted graphs, where we are given the vertex set, $V$, of a weighted graph, $G=(V,E,w)$, but we are not given $E$. The problem, which is also known as graph reconstruction, is to…
This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a…