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We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced high probability guarantees are rare, and typically either…
We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in $R^3$, (ii) reporting intersections between query lines…
We present a new analysis for QuickHeapsort splitting it into the analysis of the partition-phases and the analysis of the heap-phases. This enables us to consider samples of non-constant size for the pivot selection and leads to better…
Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works~\cite{chen2023sampling,chen2023ode,benton2023error,lee2022convergence} have proposed schemes…
Vector-based algorithms are novel algorithms in optimal any-angle path planning that are motivated by bug algorithms, bypassing free space by directly conducting line-of-sight checks between two queried points, and searching along obstacle…
Motivated by the increasing interest in applications of graph geodesic convexity in machine learning and data mining, we present a heuristic for computing the geodesic convex hull of node sets in networks. It generates a set of almost…
Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…
It has been a long time, since data mining technologies have made their ways to the field of data management. Classification is one of the most important data mining tasks for label prediction, categorization of objects into groups,…
In this work we deal with the problem of support estimation under shape restrictions. The shape restriction we deal with is an extension of the notion of convexity named alpha-convexity. Instead of assuming, as in the convex case, the…
In recent years, artificial neural networks have achieved state-of-the-art performance for predicting the responses of neurons in the visual cortex to natural stimuli. However, they require a time consuming parameter optimization process…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
Let $P$ be a set of $n$ labeled points in the plane. The radial system of $P$ describes, for each $p\in P$, the order in which a ray that rotates around $p$ encounters the points in $P \setminus \{p\}$. This notion is related to the order…
Detecting out-of-distribution (OOD) data is a critical task for maintaining model reliability and robustness. In this study, we propose a novel anomaly detection algorithm that leverages the convex hull (CH) property of a dataset by…
This paper evaluates several improvements to the memory layout of convex hulls to improve computation times for support point queries. The support point query is a fundamental part of common collision algorithms, and the work presented…
Most previous studies of the sorting algorithm QuickSort have used the number of key comparisons as a measure of the cost of executing the algorithm. Here we suppose that the n independent and identically distributed (i.i.d.) keys are each…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
The analysis of algorithms mostly relies on counting classic elementary operations like additions, multiplications, comparisons, swaps etc. This approach is often sufficient to quantify an algorithm's efficiency. In some cases, however,…