Related papers: High-Precision Framework for Expected Hitting Time…
We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…
We propose a new, data-driven approach for efficient pricing of - fixed- and float-strike - discrete arithmetic Asian and Lookback options when the underlying process is driven by the Heston model dynamics. The method proposed in this…
In this work we adapt a prediction-correction algorithm for continuous time-varying convex optimization problems to solve dynamic programs arising from Model Predictive Control. In particular, the prediction step tracks the evolution of the…
We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures the…
In this work, we present a new iterative exact solution algorithm for the weighted fair sequences problem, which is a recently introduced NP-hard sequencing problem with applications in diverse areas such as TV advertisement scheduling,…
Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…
In this article, we present a simple technique for boosting the order of accuracy of finite difference schemes for time dependent partial differential equations by optimally selecting the time step used to advance the numerical solution and…
Writing correct distributed programs is hard. In spite of extensive testing and debugging, software faults persist even in commercial grade software. Many distributed systems, especially those employed in safety-critical environments,…
Given n elements with nonnegative integer weights w1,..., wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given…
We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE…
In many important applications of precision medicine, the outcome of interest is time to an event (e.g., death, relapse of disease) and the primary goal is to identify the optimal individualized decision rule (IDR) to prolong survival time.…
In recent years, there has been growing interest in utilizing modern machine learning techniques to learn heuristic functions for forward search algorithms. Despite this, there has been little theoretical understanding of what they should…
In the 3-Hitting Set problem, the input is a hypergraph $G$ such that the size of every hyperedge of $G$ is at most 3, and an integers $k$, and the goal is to decide whether there is a set $S$ of at most $k$ vertices such that every…
We propose a simple extension of top-down decision tree learning heuristics such as ID3, C4.5, and CART. Our algorithm achieves provable guarantees for all target functions $f: \{-1,1\}^n \to \{-1,1\}$ with respect to the uniform…
We study the numerical computation of an expectation of a bounded function with respect to a measure given by a non-normalized density on a convex body. We assume that the density is log-concave, satisfies a variability condition and is not…
Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the…
The considered problem is how to optimally allocate a set of jobs to technicians of different skills such that the number of technicians of each skill does not exceed the number of persons with that skill designation. The key motivation is…
The Basic Counting problem [1] is one of the most fundamental and critical streaming problems of sliding window queries over data streams. Given a stream of 0's and 1's, the purpose of this problem is to estimate the number of 1's in the…
Hamiltonian Monte Carlo (HMC) is an efficient method of simulating smooth distributions and has motivated the widely used No-U-turn Sampler (NUTS) and software Stan. We build on NUTS and the technique of "unbiased sampling" to design HMC…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…