Related papers: Nearly Optimal Bounds for Computing Decision Tree …
Nonlinear metrics, such as the F1-score, Matthews correlation coefficient, and Fowlkes-Mallows index, are often used to evaluate the performance of machine learning models, in particular, when facing imbalanced datasets that contain more…
We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on n vertices into an O(n\log n)-edge graph on the same…
A $(1 \pm \epsilon)$-sparsifier of a hypergraph $G(V,E)$ is a (weighted) subgraph that preserves the value of every cut to within a $(1 \pm \epsilon)$-factor. It is known that every hypergraph with $n$ vertices admits a $(1 \pm…
We revisit the problem of estimating the profile (also known as the rarity) in the data stream model. Given a sequence of $m$ elements from a universe of size $n$, its profile is a vector $\phi$ whose $i$-th entry $\phi_i$ represents the…
We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…
We formulate in this paper the mini-bucket algorithm for approximate inference in terms of exact inference on an approximate model produced by splitting nodes in a Bayesian network. The new formulation leads to a number of theoretical and…
Decision trees are powerful tools for classification and regression that attract many researchers working in the burgeoning area of machine learning. One advantage of decision trees over other methods is their interpretability, which is…
Frequency estimation in data streams is one of the classical problems in streaming algorithms. Following much research, there are now almost matching upper and lower bounds for the trade-off needed between the number of samples and the…
Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been…
In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…
Assisted by the availability of data and high performance computing, deep learning techniques have achieved breakthroughs and surpassed human performance empirically in difficult tasks, including object recognition, speech recognition, and…
We consider the problem of minimizing the number of matrix-vector queries needed for accurate trace estimation in the dynamic setting where our underlying matrix is changing slowly, such as during an optimization process. Specifically, for…
Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition…
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates…
Given a graph G, the {\em maximum internal spanning tree problem} (MIST for short) asks for computing a spanning tree T of G such that the number of internal vertices in T is maximized. MIST has possible applications in the design of…
In this paper, we propose a design methodology for one-class classifiers using an ensemble-of-classifiers approach. The objective is to select the best structures created during the training phase using an ensemble of spanning trees. It…
Lipschitz decomposition is a useful tool in the design of efficient algorithms involving metric spaces. While many bounds are known for different families of finite metrics, the optimal parameters for $n$-point subsets of $\ell_p$, for $p >…
We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…
The study of optimal decision trees has gained increasing attention in recent years; however, despite substantial progress, it still suffers from two major challenges: First, trees constructed by existing optimal decision tree (ODT)…
We study the problem of approximately simulating a $t$-step random walk on a graph where the input edges come from a single-pass stream. The straightforward algorithm using reservoir sampling needs $O(nt)$ words of memory. We show that this…