Related papers: Scalable and Incremental Learning of Gaussian Mixt…
The Expectation-Maximization (EM) algorithm is a widely used method for maximum likelihood estimation in models with latent variables. For estimating mixtures of Gaussians, its iteration can be viewed as a soft version of the k-means…
Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…
3D models have recently been popularized by the potentiality of end-to-end training offered first by Neural Radiance Fields and most recently by 3D Gaussian Splatting models. The latter has the big advantage of naturally providing fast…
We propose a dynamical scaling analysis improved by a deep learning approach. While Gaussian process regression has been widely employed for estimating scaling parameters, its computational cost for parameter optimization becomes a…
The ability of artificial agents to increment their capabilities when confronted with new data is an open challenge in artificial intelligence. The main challenge faced in such cases is catastrophic forgetting, i.e., the tendency of neural…
Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…
Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
The exploration-exploitation trade-off is among the central challenges of reinforcement learning. The optimal Bayesian solution is intractable in general. This paper studies to what extent analytic statements about optimal learning are…
Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means…
In this work, we consider learning sparse models in large scale settings, where the number of samples and the feature dimension can grow as large as millions or billions. Two immediate issues occur under such challenging scenario: (i)…
We study the task of learning latent-variable models. A common algorithmic technique for this task is the method of moments. Unfortunately, moment-based approaches are hampered by the fact that the moment tensors of super-constant degree…
Variational inference with Gaussian mixture models (GMMs) enables learning of highly tractable yet multi-modal approximations of intractable target distributions with up to a few hundred dimensions. The two currently most effective methods…
Evaluating the Torontonian function is a central computational challenge in the simulation of Gaussian Boson Sampling (GBS) with threshold detection. In this work, we propose a recursive algorithm providing a polynomial speedup in the exact…
We introduce a novel sensitivity analysis framework for large scale classification problems that can be used when a small number of instances are incrementally added or removed. For quickly updating the classifier in such a situation,…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…
For future learning systems, incremental learning is desirable because it allows for: efficient resource usage by eliminating the need to retrain from scratch at the arrival of new data; reduced memory usage by preventing or limiting the…
The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…
We introduce a stochastic variational inference procedure for training scalable Gaussian process (GP) models whose per-iteration complexity is independent of both the number of training points, $n$, and the number basis functions used in…