This paper introduces an alternative approach to sampling from autoregressive models. Autoregressive models are typically sampled sequentially, according to the transition dynamics defined by the model. Instead, we propose a sampling procedure that initializes a sequence with white noise and follows a Markov chain defined by Langevin dynamics on the global log-likelihood of the sequence. This approach parallelizes the sampling process and generalizes to conditional sampling. Using an autoregressive model as a Bayesian prior, we can steer the output of a generative model using a conditional likelihood or constraints. We apply these techniques to autoregressive models in the visual and audio domains, with competitive results for audio source separation, super-resolution, and inpainting.

This paper introduces a general framework for explicitly constructing universal deep neural models with inputs from a complete, separable, and locally-compact metric space $\mathcal{X}$ and outputs in the Wasserstein-1 $\mathcal{P}_1(\mathcal{Y})$ space over a complete and separable metric space $\mathcal{Y}$. We find that any model built using the proposed framework is dense in the space $C(\mathcal{X},\mathcal{P}_1(\mathcal{Y}))$ of continuous functions from $\mathcal{X}$ to $\mathcal{P}_1(\mathcal{Y})$ in the corresponding uniform convergence on compacts topology, quantitatively. We identify two methods in which the curse of dimensionality can be broken. The first approach constructs subsets of $C(\mathcal{X},\mathcal{P}_1(\mathcal{Y}))$ consisting of functions that can be efficiently approximated. In the second approach, given any fixed $f \in C(\mathcal{X},\mathcal{P}_1(\mathcal{Y}))$, we build non-trivial subsets of $\mathcal{X}$ on which $f$ can be efficiently approximated. The results are applied to three open problems lying at the interface of applied probability and computational learning theory. We find that the proposed models can approximate any regular conditional distribution of a $\mathcal{Y}$-valued random element $Y$ depending on an $\mathcal{X}$-valued random element $X$, with arbitrarily high probability. The proposed models are also shown to be capable of generically expressing the aleatoric uncertainty present in most randomized machine learning models. The proposed framework is used to derive an affirmative answer to the open conjecture of Bishop (1994); namely: mixture density networks are generic regular conditional distributions. Numerical experiments are performed in the contexts of extreme learning machines, randomized DNNs, and heteroscedastic regression.

This study investigates the theoretical foundations of t-distributed stochastic neighbor embedding (t-SNE), a popular nonlinear dimension reduction and data visualization method. A novel theoretical framework for the analysis of t-SNE based on the gradient descent approach is presented. For the early exaggeration stage of t-SNE, we show its asymptotic equivalence to a power iteration based on the underlying graph Laplacian, characterize its limiting behavior, and uncover its deep connection to Laplacian spectral clustering, and fundamental principles including early stopping as implicit regularization. The results explain the intrinsic mechanism and the empirical benefits of such a computational strategy. For the embedding stage of t-SNE, we characterize the kinematics of the low-dimensional map throughout the iterations, and identify an amplification phase, featuring the intercluster repulsion and the expansive behavior of the low-dimensional map. The general theory explains the fast convergence rate and the exceptional empirical performance of t-SNE for visualizing clustered data, brings forth the interpretations of the t-SNE output, and provides theoretical guidance for selecting tuning parameters in various applications.

In multistage manufacturing systems, modeling multiple quality indices based on the process sensing variables is important. However, the classic modeling technique predicts each quality variable one at a time, which fails to consider the correlation within or between stages. We propose a deep multistage multi-task learning framework to jointly predict all output sensing variables in a unified end-to-end learning framework according to the sequential system architecture in the MMS. Our numerical studies and real case study have shown that the new model has a superior performance compared to many benchmark methods as well as great interpretability through developed variable selection techniques.

The framework is founded on an approach of minimising the Kullback-Leibler (KL) divergence between a variational solution and the posterior, in a constrained space. The works (Dudík et al., 2004, 2007; Altun and Smola, 2006) first raised the idea of including constraints in maximum entropy density estimation and provided a theoretical analysis. Based on convex duality theory, the optimal solution of the regularised posterior is found to be the original posterior of the model, discounted by the constrained pseudo likelihood introduced by the constraints. Later work founded on the idea of posterior constraints includes (Graça et al., 2009) which proposed constraining the E-step of an Expectation-maximization (EM) algorithm, in order to impose feature constraints on the solution.

Machine learning algorithms have gained fame for being able to ferret out relevant information from datasets with many features, such as tables with dozens of rows and images with millions of pixels. Thanks to advances in cloud computing, you can often run very large machine learning models without noticing how much computational power works behind the scenes. But every new feature that you add to your problem adds to its complexity, making it harder to solve it with machine learning algorithms. Data scientists use dimensionality reduction, a set of techniques that remove excessive and irrelevant features from their machine learning models. Dimensionality reduction slashes the costs of machine learning and sometimes makes it possible to solve complicated problems with simpler models.

We see that column "Post Weekday" has less variance and column "Lifetime Post Total Reach" has comparatively more variance. Therefore, if we apply PCA without standardization of data then more weightage will be given to the "Lifetime Post Total Reach" column during the calculation of "eigenvectors" and "eigenvalues" and we will get biased principal components. Now we will standardize the dataset using RobustScaler of sklearn library. Other ways of standardizing data are provided in sklearn like StandardScaler and MinMaxScaler and can be chosen as per the requirement. Unless specified, the number of principal components will be equal to the number of attributes.

In my August 2020 article, "How to choose a cloud Machine Learning platform," my first guideline for choosing a platform was, "Be close to your data." Keeping the code near the data is necessary to keep the latency low, since the speed of light limits transmission speeds. After all, machine learning -- especially deep learning -- tends to go through all your data multiple times (each time through is called an epoch). I said at the time that the ideal case for very large data sets is to build the model where the data already resides, so that no mass data transmission is needed. Several databases support that to a limited extent.

Predictive Analytics is a division of advanced analytics which is used to forecast uncertain future events. Predictive analytics make use of an array of technologies from different domains such as data mining, statistics, modeling, machine learning, and artificial intelligence to analyze historic data to forecast the future. It uses a stack of data mining, predictive modeling and analytical methodologies to bring together the management, information technology, and modeling business process to forecast the future. The historical and transactional patterns of data can be used for risk identification and future opportunities. Predictive analytics models detect correlation among many factors to assess risk with a particular set of conditions to give a score or weightage.

To accurately pour drinks into various containers is an essential skill for service robots. However, drink pouring is a dynamic process and difficult to model. Traditional deep imitation learning techniques for implementing autonomous robotic pouring have an inherent black-box effect and require a large amount of demonstration data for model training. To address these issues, an Explainable Hierarchical Imitation Learning (EHIL) method is proposed in this paper such that a robot can learn high-level general knowledge and execute low-level actions across multiple drink pouring scenarios. Moreover, with EHIL, a logical graph can be constructed for task execution, through which the decision-making process for action generation can be made explainable to users and the causes of failure can be traced out. Based on the logical graph, the framework is manipulable to achieve different targets while the adaptability to unseen scenarios can be achieved in an explainable manner. A series of experiments have been conducted to verify the effectiveness of the proposed method. Results indicate that EHIL outperforms the traditional behavior cloning method in terms of success rate, adaptability, manipulability and explainability.