(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative ways to optimize the functional. In particular, we identify various gradient flows associated with $F$ and show that their limits coincide with $F$'s stationary points. By discretizing the flows, we obtain practical particle-based algorithms for maximum likelihood estimation in broad classes of latent variable models. The novel algorithms scale to high-dimensional settings and perform well in numerical experiments.

Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the posterior predictive of the Dirichlet process mixture model. In general, direct estimation of the posterior predictive is intractable and so methods typically resort to approximating the posterior distribution as an intermediate step. The recent development of quasi-Bayesian predictive copula updates, however, has made it possible to perform tractable predictive density estimation without the need for posterior approximation. Although these estimators are computationally appealing, they tend to struggle on non-smooth data distributions. This is due to the comparatively restrictive form of the likelihood models from which the proposed copula updates were derived. To address this shortcoming, we consider a Bayesian nonparametric model with an autoregressive likelihood decomposition and a Gaussian process prior. While the predictive update of such a model is typically intractable, we derive a quasi-Bayesian predictive update that achieves state-of-the-art results in small-data regimes.

Diffusion-based generative models are a design framework that allows generating new images from processes analogous to those found in non-equilibrium thermodynamics. These models model the reversal of a physical diffusion process in which two miscible liquids of different colors progressively mix until they form a homogeneous mixture. Diffusion models can be applied to signals of a different nature, such as audio and image signals. In the image case, a progressive pixel corruption process is carried out by applying random noise, and a neural network is trained to revert each one of the corruption steps. For the reconstruction process to be reversible, it is necessary to carry out the corruption very progressively. If the training of the neural network is successful, it will be possible to generate an image from random noise by chaining a number of steps similar to those used for image deconstruction at training time. In this article we present the theoretical foundations on which this method is based as well as some of its applications. This article is in Spanish to facilitate the arrival of this scientific knowledge to the Spanish-speaking community.

The sole aim of this book is to give a self-contained introduction to concepts and mathematical tools in Bayesian matrix decomposition in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning Bayesian matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of variational inference for conducting the optimization. We refer the reader to literature in the field of Bayesian analysis for a more detailed introduction to the related fields. This book is primarily a summary of purpose, significance of important Bayesian matrix decomposition methods, e.g., real-valued decomposition, nonnegative matrix factorization, Bayesian interpolative decomposition, and the origin and complexity of the methods which shed light on their applications. The mathematical prerequisite is a first course in statistics and linear algebra. Other than this modest background, the development is self-contained, with rigorous proof provided throughout.

Efficient road and building footprint extraction from satellite images are predominant in many remote sensing applications. However, precise segmentation map extraction is quite challenging due to the diverse building structures camouflaged by trees, similar spectral responses between the roads and buildings, and occlusions by heterogeneous traffic over the roads. Existing convolutional neural network (CNN)-based methods focus on either enriched spatial semantics learning for the building extraction or the fine-grained road topology extraction. The profound semantic information loss due to the traditional pooling mechanisms in CNN generates fragmented and disconnected road maps and poorly segmented boundaries for the densely spaced small buildings in complex surroundings. In this paper, we propose a novel attention-aware segmentation framework, Multi-Scale Supervised Dilated Multiple-Path Attention Network (MSSDMPA-Net), equipped with two new modules Dynamic Attention Map Guided Index Pooling (DAMIP) and Dynamic Attention Map Guided Spatial and Channel Attention (DAMSCA) to precisely extract the building footprints and road maps from remotely sensed images. DAMIP mines the salient features by employing a novel index pooling mechanism to retain important geometric information. On the other hand, DAMSCA simultaneously extracts the multi-scale spatial and spectral features. Besides, using dilated convolution and multi-scale deep supervision in optimizing MSSDMPA-Net helps achieve stellar performance. Experimental results over multiple benchmark building and road extraction datasets, ensures MSSDMPA-Net as the state-of-the-art (SOTA) method for building and road extraction.

Unmanned Aerial Vehicles (UAVs) are widely used and meet many demands in military and civilian fields. With the continuous enrichment and extensive expansion of application scenarios, the safety of UAVs is constantly being challenged. To address this challenge, we propose algorithms to detect anomalous data collected from drones to improve drone safety. We deployed a one-class kernel extreme learning machine (OCKELM) to detect anomalies in drone data. By default, OCKELM uses the radial basis (RBF) kernel function as the kernel function of the model. To improve the performance of OCKELM, we choose a Triangular Global Alignment Kernel (TGAK) instead of an RBF Kernel and introduce the Fast Independent Component Analysis (FastICA) algorithm to reconstruct UAV data. Based on the above improvements, we create a novel anomaly detection strategy FastICA-TGAK-OCELM. The method is finally validated on the UCI dataset and detected on the Aeronautical Laboratory Failures and Anomalies (ALFA) dataset. The experimental results show that compared with other methods, the accuracy of this method is improved by more than 30%, and point anomalies are effectively detected.

Future AI applications require performance, reliability and privacy that the existing, cloud-dependant system architectures cannot provide. In this article, we study orchestration in the device-edge-cloud continuum, and focus on edge AI for resource orchestration. We claim that to support the constantly growing requirements of intelligent applications in the device-edge-cloud computing continuum, resource orchestration needs to embrace edge AI and emphasize local autonomy and intelligence. To justify the claim, we provide a general definition for continuum orchestration, and look at how current and emerging orchestration paradigms are suitable for the computing continuum. We describe certain major emerging research themes that may affect future orchestration, and provide an early vision of an orchestration paradigm that embraces those research themes. Finally, we survey current key edge AI methods and look at how they may contribute into fulfilling the vision of future continuum orchestration.

In this paper, we present a novel model-agnostic machine learning technique to extract a reduced thermochemical model for reacting hypersonic flows simulation. A first simulation gathers all relevant thermodynamic states and the corresponding gas properties via a given model. The states are embedded in a low-dimensional space and clustered to identify regions with different levels of thermochemical (non)-equilibrium. Then, a surrogate surface from the reduced cluster-space to the output space is generated using radial-basis-function networks. The method is validated and benchmarked on a simulation of a hypersonic flat-plate boundary layer with finite-rate chemistry. The gas properties of the reactive air mixture are initially modeled using the open-source Mutation++ library. Substituting Mutation++ with the light-weight, machine-learned alternative improves the performance of the solver by 50% while maintaining overall accuracy.

Diffusion models generate samples by reversing a fixed forward diffusion process. Despite already providing impressive empirical results, these diffusion models algorithms can be further improved by reducing the variance of the training targets in their denoising score-matching objective. We argue that the source of such variance lies in the handling of intermediate noise-variance scales, where multiple modes in the data affect the direction of reverse paths. We propose to remedy the problem by incorporating a reference batch which we use to calculate weighted conditional scores as more stable training targets. We show that the procedure indeed helps in the challenging intermediate regime by reducing (the trace of) the covariance of training targets. The new stable targets can be seen as trading bias for reduced variance, where the bias vanishes with increasing reference batch size. Empirically, we show that the new objective improves the image quality, stability, and training speed of various popular diffusion models across datasets with both general ODE and SDE solvers. When used in combination with EDM, our method yields a current SOTA FID of 1.90 with 35 network evaluations on the unconditional CIFAR-10 generation task. The code is available at https://github.com/Newbeeer/stf

Imperfect score-matching leads to a shift between the training and the sampling distribution of diffusion models. Due to the recursive nature of the generation process, errors in previous steps yield sampling iterates that drift away from the training distribution. Yet, the standard training objective via Denoising Score Matching (DSM) is only designed to optimize over non-drifted data. To train on drifted data, we propose to enforce a \emph{consistency} property which states that predictions of the model on its own generated data are consistent across time. Theoretically, we show that if the score is learned perfectly on some non-drifted points (via DSM) and if the consistency property is enforced everywhere, then the score is learned accurately everywhere. Empirically we show that our novel training objective yields state-of-the-art results for conditional and unconditional generation in CIFAR-10 and baseline improvements in AFHQ and FFHQ. We open-source our code and models: https://github.com/giannisdaras/cdm