Stochastic latent variable models (LVMs) achieve state-of-the-art performance on natural image generation but are still inferior to deterministic models on speech. In this paper, we develop a speech benchmark of popular temporal LVMs and compare them against state-of-the-art deterministic models. We report the likelihood, which is a much used metric in the image domain, but rarely, or incomparably, reported for speech models. To assess the quality of the learned representations, we also compare their usefulness for phoneme recognition. Finally, we adapt the Clockwork VAE, a state-of-the-art temporal LVM for video generation, to the speech domain. Despite being autoregressive only in latent space, we find that the Clockwork VAE can outperform previous LVMs and reduce the gap to deterministic models by using a hierarchy of latent variables.

The importance of accurately quantifying forecast uncertainty has motivated much recent research on probabilistic forecasting. In particular, a variety of deep learning approaches has been proposed, with forecast distributions obtained as output of neural networks. These neural network-based methods are often used in the form of an ensemble based on multiple model runs from different random initializations, resulting in a collection of forecast distributions that need to be aggregated into a final probabilistic prediction. With the aim of consolidating findings from the machine learning literature on ensemble methods and the statistical literature on forecast combination, we address the question of how to aggregate distribution forecasts based on such deep ensembles. Using theoretical arguments, simulation experiments and a case study on wind gust forecasting, we systematically compare probability- and quantile-based aggregation methods for three neural network-based approaches with different forecast distribution types as output. Our results show that combining forecast distributions can substantially improve the predictive performance. We propose a general quantile aggregation framework for deep ensembles that shows superior performance compared to a linear combination of the forecast densities. Finally, we investigate the effects of the ensemble size and derive recommendations of aggregating distribution forecasts from deep ensembles in practice.

Before we understand more about Logistic Regression, let's first recap some important definitions which will give us a better understanding of the topic. Logistic Regression comes under Supervised Learning. Supervised Learning is when the algorithm learns on a labeled dataset and analyses the training data. These labeled data sets have inputs and expected outputs. Supervised learning can be further split into classification and regression. Classification is about predicting a label, by identifying which category an object belongs to based on different parameters.

This article explains what data engineers are and what their varied tasks and duties are. Seaborn is a very prominent library used during Exploratory Data Analysis of any data science project you are working upon. At times, this cohort could feel overwhelming due to the sheer volume of material I would need to learn and practice.

The Yellowbrick library also contains a set of visualisation tools for analysing clustering algorithms. A common way to evaluate the performance of clustering models is with an intercluster distance map. The intercluster distance map plots an embedding of each cluster centre and visualises both the distance between the clusters and the relative size of each cluster based on membership. We can turn the diabetes dataset into a clustering problem by only using the features (X). Before we cluster the data we can use the popular elbow method to find the optimal number of clusters.

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes stochastic, and more precisely discretely indexed. Due to the discrete nature of the underlying additional latent variable, DIF inherit the good computational behavior of NF: they benefit from both a tractable density as well as a straightforward sampling scheme, and can thus be used for the dual problems of Variational Inference (VI) and of Variational density estimation (VDE). On the other hand, DIF can also be understood as an extension of mixture density models, in which the constant mixture weights are replaced by flexible functions. As a consequence, DIF are better suited for capturing distributions with discontinuities, sharp edges and fine details, which is a main advantage of this construction. Finally we propose a methodology for constructiong DIF in practice, and see that DIF can be sequentially cascaded, and cascaded with NF.

In the previous tutorial here on SGD, I explored the way in which we can implement using PyTorch's built-in gradient calculation, loss, and optimization implementation. in our present discussion…

Today, various machine learning (ML) applications offer continuous data processing and real-time data analytics at the edge of a wireless network. Distributed real-time ML solutions are highly sensitive to the so-called straggler effect caused by resource heterogeneity and alleviated by various computation offloading mechanisms that seriously challenge the communication efficiency, especially in large-scale scenarios. To decrease the communication overhead, we rely on device-to-device (D2D) connectivity that improves spectrum utilization and allows efficient data exchange between devices in proximity. In particular, we design a novel D2D-aided coded federated learning method (D2D-CFL) for efficient load balancing across devices. The proposed solution captures system dynamics, including data (time-dependent learning model, varied intensity of data arrivals), device (diverse computational resources and volume of training data), and deployment (varied locations and D2D graph connectivity). To minimize the number of communication rounds, we derive an optimal compression rate for achieving minimum processing time and establish its connection with the convergence time. The resulting optimization problem provides suboptimal compression parameters, which improve the total training time. Our proposed method is beneficial for real-time collaborative applications, where the users continuously generate training data resulting in the model drift.

It is common in machine learning and statistics to use symmetries derived from expert knowledge to simplify problems or improve performance, using methods like data augmentation or penalties. In this paper we consider the unsupervised and semi-supervised problems of learning such symmetries in a distribution directly from data in a model-free fashion. We show that in the worst case this problem is as difficult as the graph automorphism problem. However, if we restrict to the case where the covariance matrix has unique eigenvalues, then the eigenvectors will also be eigenvectors of the symmetry transformation. If we further restrict to finding orthogonal symmetries, then the eigenvalues will be either be 1 or -1, and the problem reduces to determining which eigenvectors are which. We develop and compare theoretically and empirically the effectiveness of different methods of selecting which eigenvectors should have eigenvalue -1 in the symmetry transformation, and discuss how to extend this approach to non-orthogonal cases where we have labels

In a neural network, there is the concept of loss, which is used to calculate performance. The higher the loss, the poorer the performance of the neural network, that is why we always try to minimize the loss so that the neural network performs better. The process of minimizing loss is called optimization. An optimizer is a method that modifies the weights of the neural network to reduce the loss. Although several neural network optimizers exist, in this article we will learn about gradient descent with momentum and compare its performance with others.