相关论文: Stronger Coreset Bounds for Kernel Density Estimat…
We propose a family of recursive cutting-plane algorithms to solve feasibility problems with constrained memory, which can also be used for first-order convex optimization. Precisely, in order to find a point within a ball of radius…
Given a set of points in a metric space, the $(k,z)$-clustering problem consists of finding a set of $k$ points called centers, such that the sum of distances raised to the power of $z$ of every data point to its closest center is…
We derive approximation bounds for learning single neuron models using thresholded gradient descent when both the labels and the covariates are possibly corrupted adversarially. We assume the data follows the model $y =…
Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, i.e., irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They…
We provide general lower and upper bounds for Laplace Dirichlet heat kernel of convex $\mathcal C^{1,1}$ domains. The obtained estimates precisely describe the exponential behaviour of the kernels, which has been known only in a few special…
Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…
We introduce CO2, an efficient algorithm to produce convexly-weighted coresets with respect to generic smooth divergences. By employing a functional Taylor expansion, we show a local equivalence between sufficiently regular losses and their…
We study monotonicity testing of functions $f \colon \{0,1\}^d \to \{0,1\}$ using sample-based algorithms, which are only allowed to observe the value of $f$ on points drawn independently from the uniform distribution. A classic result by…
A coreset is a point set containing information about geometric properties of a larger point set. A series of previous works show that in many machine learning problems, especially in clustering problems, coreset could be very useful to…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
The Johnson-Lindenstrauss transform is a fundamental method for dimension reduction in Euclidean spaces, that can map any dataset of $n$ points into dimension $O(\log n)$ with low distortion of their distances. This dimension bound is tight…
Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…
Uniform sampling is a highly efficient method for data summarization. However, its effectiveness in producing coresets for clustering problems is not yet well understood, primarily because it generally does not yield a strong coreset, which…
Given a dataset of $n$ user-contributed strings, each of length at most $\ell$, a key problem is how to identify all frequent substrings while preserving each user's privacy. Recent work by Bernardini et al. (PODS'25) introduced a…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
We introduce a new quantum optimization algorithm for dense Linear Programming problems, which can be seen as the quantization of the Interior Point Predictor-Corrector algorithm \cite{Predictor-Corrector} using a Quantum Linear System…
We study distributed similarity estimation of quantum channels (DSEC), a primitive for cross-platform verification where two remote quantum devices are compared by estimating the inner product of their Choi states. We show that the optimal…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
We consider tensor product random fields $Y_d$, $d\in\mathbb{N}$, whose covariance funtions are Gaussian kernels. The average case approximation complexity $n^{Y_d}(\varepsilon)$ is defined as the minimal number of evaluations of arbitrary…
Combining Gaussian processes with the expressive power of deep neural networks is commonly done nowadays through deep kernel learning (DKL). Unfortunately, due to the kernel optimization process, this often results in losing their Bayesian…