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Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen…
Introduced over a century ago, Whittaker-Henderson smoothing remains widely used by actuaries in constructing one-dimensional and two-dimensional experience tables for mortality, disability and other life insurance risks. In this paper, we…
The performance of standard stochastic approximation implementations can vary significantly based on the choice of the steplength sequence, and in general, little guidance is provided about good choices. Motivated by this gap, in the first…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
Gradient descent and stochastic gradient descent are central to modern machine learning, yet their behavior under large step sizes remains theoretically unclear. Recent work suggests that acceleration often arises near the edge of…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
We introduce neural particle smoothing, a sequential Monte Carlo method for sampling annotations of an input string from a given probability model. In contrast to conventional particle filtering algorithms, we train a proposal distribution…
A prevalent problem in general state-space models is the approximation of the smoothing distribution of a state, or a sequence of states, conditional on the observations from the past, the present, and the future. The aim of this paper is…
Ausgehend von einer konkreten technischen Fragestellung diskutieren wir in dieser Notiz die Anwendung verschiedener Gl\"attungsverfahren auf Datens\"atze mit vorgegebener Struktur. Wir stellen die Verfahren im Detail vor und besprechen die…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…
Randomized smoothing is the current state-of-the-art defense with provable robustness against $\ell_2$ adversarial attacks. Many works have devised new randomized smoothing schemes for other metrics, such as $\ell_1$ or $\ell_\infty$;…
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…
Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting…
Diffusion models have achieved state-of-the-art performance, demonstrating remarkable generalisation capabilities across diverse domains. However, the mechanisms underpinning these strong capabilities remain only partially understood. A…
This letter is concerned with solving continuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In the proposed smoothing method, we apply the TME method to approximate the transition density of the…
SMOTE (Synthetic Minority Oversampling Technique) is the established geometric approach to random oversampling to balance classes in the imbalanced learning problem, followed by many extensions. Its idea is to introduce synthetic data…
We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented via an exponential formula at a later time. The time-dependent generator of this exponential operator only depends…
Before entering the neural network, a token is generally converted to the corresponding one-hot representation, which is a discrete distribution of the vocabulary. Smoothed representation is the probability of candidate tokens obtained from…
The Sylvester smallest enclosing circle problem involves finding the smallest circle that encloses a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets.…