Related papers: Query Complexity of k-NN based Mode Estimation

Approximate K nearest neighbor (AKNN) search is a fundamental and challenging problem. We observe that in high-dimensional space, the time consumption of nearly all AKNN algorithms is dominated by that of the distance comparison operations…

$k$-nearest neighbor classification is a popular non-parametric method because of desirable properties like automatic adaption to distributional scale changes. Unfortunately, it has thus far proved difficult to design active learning…

Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…

The approximate degree of a Boolean function is the minimum degree of real polynomial that approximates it pointwise. For any Boolean function, its approximate degree serves as a lower bound on its quantum query complexity, and generically…

When applying outlier detection in settings where data is sensitive, mechanisms which guarantee the privacy of the underlying data are needed. The $k$-nearest neighbors ($k$-NN) algorithm is a simple and one of the most effective methods…

We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…

The Reverse $k$-Nearest Neighbor (R$k$NN) query over moving objects on road networks seeks to find all moving objects that consider the specified query point as one of their $k$ nearest neighbors. In location based services, many users…

We consider the problem of uncertainty quantification in change point regressions, where the signal can be piecewise polynomial of arbitrary but fixed degree. That is we seek disjoint intervals which, uniformly at a given confidence level,…

Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb{R}^{d}$ with an optimal number of samples. We generalize this problem to the case of spatial signals,…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…

Given two distributions $\mathcal{P}$ and $\mathcal{Q}$ over a high-dimensional domain $\{0,1\}^n$, and a parameter $\varepsilon$, the goal of distance estimation is to determine the statistical distance between $\mathcal{P}$ and…

There is a rich literature on Bayesian methods for density estimation, which characterize the unknown density as a mixture of kernels. Such methods have advantages in terms of providing uncertainty quantification in estimation, while being…

Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours…

We study the problem of learning an unknown mixture of $k$ rankings over $n$ elements, given access to noisy samples drawn from the unknown mixture. We consider a range of different noise models, including natural variants of the "heat…

Using the 20 questions estimation framework with query-dependent noise, we study non-adaptive search strategies for a moving target over the unit cube with unknown initial location and velocities under a piecewise constant velocity model.…

Consider that the coordinates of $N$ points are randomly generated along the edges of a $d$-dimensional hypercube (random point problem). The probability that an arbitrary point is the $m$th nearest neighbor to its own $n$th nearest…

Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled…

Navigating an environment with uncertain connectivity requires a strategic balance between minimizing the cost of traversal and seeking information to resolve map ambiguities. Unlike previous approaches that rely on local sensing, we…