Related papers: Statistical Inference for Online Algorithms
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
This paper introduces a local optimization-based approach to test statistical hypotheses and to construct confidence intervals. This approach can be viewed as an extension of bootstrap, and yields asymptotically valid tests and confidence…
Active statistical inference is a new method for inference with AI-assisted data collection. Given a budget on the number of labeled data points that can be collected and assuming access to an AI predictive model, the basic idea is to…
We focus on interval algorithms for computing guaranteed enclosures of the solutions of constrained global optimization problems where differential constraints occur. To solve such a problem of global optimization with nonlinear ordinary…
Randomized quasi-Monte Carlo (RQMC) methods estimate the mean of a random variable by sampling an integrand at $n$ equidistributed points. For scrambled digital nets, the resulting variance is typically $\tilde O(n^{-\theta})$ where…
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we…
Machine learning optimization often depends on stochastic gradient descent, where the precision of gradient estimation is vital for model performance. Gradients are calculated from mini-batches formed by uniformly selecting data samples…
Bayesian inference is a principled framework for dealing with uncertainty. The practitioner can perform an initial assumption for the physical phenomenon they want to model (prior belief), collect some data and then adjust the initial…
In this paper, an online learning algorithm is proposed as sequential stochastic approximation of a regularization path converging to the regression function in reproducing kernel Hilbert spaces (RKHSs). We show that it is possible to…
The goal of nonparametric regression is to recover an underlying regression function from noisy observations, under the assumption that the regression function belongs to a pre-specified infinite dimensional function space. In the online…
Based on binary inquiries, we developed an algorithm to estimate population quantiles under Local Differential Privacy (LDP). By self-normalizing, our algorithm provides asymptotically normal estimation with valid inference, resulting in…
This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs that depend on random variables with decision-dependent distributions. In this context, we propose the use of an online…
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions…
This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
Monte Carlo inference has asymptotic guarantees, but can be slow when using generic proposals. Handcrafted proposals that rely on user knowledge about the posterior distribution can be efficient, but are difficult to derive and implement.…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
Machine learning classifiers are probabilistic in nature, and thus inevitably involve uncertainty. Predicting the probability of a specific input to be correct is called uncertainty (or confidence) estimation and is crucial for risk…
Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat…
The goal of regression is to recover an unknown underlying function that best links a set of predictors to an outcome from noisy observations. In nonparametric regression, one assumes that the regression function belongs to a pre-specified…