相关论文: Thresholding in Learning Theory
The level set estimation problem seeks to find all points in a domain ${\cal X}$ where the value of an unknown function $f:{\cal X}\rightarrow \mathbb{R}$ exceeds a threshold $\alpha$. The estimation is based on noisy function evaluations…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…
Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al.…
In this paper, we investigate a problem of actively learning threshold in latent space, where the unknown reward $g(\gamma, v)$ depends on the proposed threshold $\gamma$ and latent value $v$ and it can be $only$ achieved if the threshold…
We consider a setting for Inverse Reinforcement Learning (IRL) where the learner is extended with the ability to actively select multiple environments, observing an agent's behavior on each environment. We first demonstrate that if the…
Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the…
We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$. Because proper learning procedures, i.e., procedures that are only allowed to select functions in $F$, tend to perform poorly unless…
This paper describes a new form of unsupervised learning, whose input is a set of unlabeled points that are assumed to be local maxima of an unknown value function v in an unknown subset of the vector space. Two functions are learned: (i) a…
We study the problem of approximating and estimating classification functions that have their decision boundary in the $RBV^2$ space. Functions of $RBV^2$ type arise naturally as solutions of regularized neural network learning problems and…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…
Machine learning has witnessed tremendous success in solving tasks depending on a single hyperparameter. When considering simultaneously a finite number of tasks, multi-task learning enables one to account for the similarities of the tasks…
Most modern neural networks for classification fail to take into account the concept of the unknown. Trained neural networks are usually tested in an unrealistic scenario with only examples from a closed set of known classes. In an attempt…
Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the independent and Markovian observation settings. In particular,…
Most machine learning theory and practice is concerned with learning a single task. In this thesis it is argued that in general there is insufficient information in a single task for a learner to generalise well and that what is required…
Level set estimation (LSE) classifies whether an unknown function's value exceeds a specified threshold for given inputs, a fundamental problem in many real-world applications. In active learning settings with limited initial data, we aim…
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…