Related papers: The Careless Coupon Collector's Problem
We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…
Online electronic coupon (e-coupon) is becoming a primary tool for e-commerce platforms to attract users to place orders. E-coupons are the digital equivalent of traditional paper coupons which provide customers with discounts or gifts. One…
We prove that, in the coupon collector's problem, the point processes given by the times of $r$-th arrivals for coupons of each type, centered and normalized in a proper way, converge toward a non-homogeneous Poisson point process. This…
For status update systems operating over unreliable energy-constrained wireless channels, we address Weaver's long-standing Level-C question: do my packets actually improve the plant's behavior? Each fresh sample carries a stochastic…
Despite the coupon collector's problem has simple probabilistic solution using inclusion/exclusion principle \cite{PolyaUrn}, starting from a particular type of recurrence differential equation it is used an analytic approach to recover…
Recently, order-preserving pattern (OPP) mining has been proposed to discover some patterns, which can be seen as trend changes in time series. Although existing OPP mining algorithms have achieved satisfactory performance, they discover…
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…
Online conformal prediction (OCP) seeks prediction intervals that achieve long-run $1-\alpha$ coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
Standard online change point detection (CPD) methods tend to have large false discovery rates as their detections are sensitive to outliers. To overcome this drawback, we propose Greedy Online Change Point Detection (GOCPD), a…
We introduce and study a novel generalization of the classical Knapsack Problem (KP), called the Colored Knapsack Problem (CKP). In this problem, the items are partitioned into classes of colors and the packed items need to be ordered such…
Coding over subsets (known as generations) rather than over all content blocks in P2P distribution networks and other applications is necessary for a number of practical reasons such as computational complexity. A penalty for coding only…
Although a concept class may be learnt more efficiently using quantum samples as compared with classical samples in certain scenarios, Arunachalam and de Wolf (JMLR, 2018) proved that quantum learners are asymptotically no more efficient…
In this paper, we consider the $k$-Covering Canadian Traveller Problem ($k$-CCTP), which can be seen as a variant of the Travelling Salesperson Problem. The goal of $k$-CCTP is finding the shortest tour for a traveller to visit a set of…
We consider a variant of the set covering problem with uncertain parameters, which we refer to as the chance-constrained set multicover problem (CC-SMCP). In this problem, we assume that there is uncertainty regarding whether a selected set…
The travelling thief problem (TTP) is a representative of multi-component optimisation problems with interacting components. TTP combines the knapsack problem (KP) and the travelling salesman problem (TSP). A thief performs a cyclic tour…
A travelling thief problem (TTP) is a proxy to real-life problems such as postal collection. TTP comprises an entanglement of a travelling salesman problem (TSP) and a knapsack problem (KP) since items of KP are scattered over cities of…
Correlation clustering is arguably the most natural formulation of clustering. Given n objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same…
We consider the sorted top-$k$ problem whose goal is to recover the top-$k$ items with the correct order out of $n$ items using pairwise comparisons. In many applications, multiple rounds of interaction can be costly. We restrict our…
When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$, Conformal Prediction (CP) is a methodology that allows to estimate a confidence set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of the…