Deep learning is a form of machine learning which allows a computer to learn from experience and understand things from a hierarchy of concepts where each concept being defined from a simpler one. This approach avoids the need for humans to specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them on top of each other through a deep setup with many layers. The first thing you need to learn when it comes to learning deep learning is the applied math which is the fundamental building block of deep learning. Linear algebra is a branch of mathematics that is widely used throughout engineering.

The neural attention mechanism has been incorporated into deep neural networks to achieve state-of-the-art performance in various domains. Most such models use multi-head self-attention which is appealing for the ability to attend to information from different perspectives. This paper introduces alignment attention that explicitly encourages self-attention to match the distributions of the key and query within each head. The resulting alignment attention networks can be optimized as an unsupervised regularization in the existing attention framework. It is simple to convert any models with self-attention, including pre-trained ones, to the proposed alignment attention. On a variety of language understanding tasks, we show the effectiveness of our method in accuracy, uncertainty estimation, generalization across domains, and robustness to adversarial attacks. We further demonstrate the general applicability of our approach on graph attention and visual question answering, showing the great potential of incorporating our alignment method into various attention-related tasks.

We consider the use of deep learning for parameter estimation. We propose Bias Constrained Estimators (BCE) that add a squared bias term to the standard mean squared error (MSE) loss. The main motivation to BCE is learning to estimate deterministic unknown parameters with no Bayesian prior. Unlike standard learning based estimators that are optimal on average, we prove that BCEs converge to Minimum Variance Unbiased Estimators (MVUEs). We derive closed form solutions to linear BCEs. These provide a flexible bridge between linear regrssion and the least squares method. In non-linear settings, we demonstrate that BCEs perform similarly to MVUEs even when the latter are computationally intractable. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance. Examples include distributed sensor networks and data augmentation in test-time. In such applications, unbiasedness is a necessary condition for asymptotic consistency.

Box-Cox transformation is commonly used remedy when the normality is not met. This comherensive guide includes estimation techniques and use of Box-Cox transformation in practice. Find out how to apply Box-Cox transformation in R. In this tutorial, we will work on Box-Cox transformation in R. Firstly, we will mention two types of estimation techniques for Box-Cox transformation parameter. These are maximum likelihood estimation (MLE) and estimation via normality tests. Secondly, we will work how to apply Box-Cox transformation in practice.

With more and more data, machine learning is becoming incredibly powerful to make more accurate predictions or personalized suggestions. However, there is no one machine learning algorithm that works best for every problem; especially, if it's for supervised learning (i.e. In this post, we will go through the basic statistical models and most common machine learning algorithms that you must know as a beginner. For the absolute beginners, please refer to this introductory article on machine learning and artificial intelligence. Machine Learning algorithms are the brains behind any model, allowing machines to learn, making them smarter.

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success in adopting a deep network for feature extraction followed by a GP used as function model. Recently,it was suggested that, albeit training with marginal likelihood, the deterministic nature of feature extractor might lead to overfitting while the replacement with a Bayesian network seemed to cure it. Here, we propose the conditional Deep Gaussian Process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. We follow our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We shall show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.

Humans are expert explorers. Understanding the computational cognitive mechanisms that support this efficiency can advance the study of the human mind and enable more efficient exploration algorithms. We hypothesize that humans explore new environments efficiently by inferring the structure of unobserved spaces using spatial information collected from previously explored spaces. This cognitive process can be modeled computationally using program induction in a Hierarchical Bayesian framework that explicitly reasons about uncertainty with strong spatial priors. Using a new behavioral Map Induction Task, we demonstrate that this computational framework explains human exploration behavior better than non-inductive models and outperforms state-of-the-art planning algorithms when applied to a realistic spatial navigation domain.

Discrete data are abundant and often arise as counts or rounded data. However, even for linear regression models, conjugate priors and closed-form posteriors are typically unavailable, thereby necessitating approximations or Markov chain Monte Carlo for posterior inference. For a broad class of count and rounded data regression models, we introduce conjugate priors that enable closed-form posterior inference. Key posterior and predictive functionals are computable analytically or via direct Monte Carlo simulation. Crucially, the predictive distributions are discrete to match the support of the data and can be evaluated or simulated jointly across multiple covariate values. These tools are broadly useful for linear regression, nonlinear models via basis expansions, and model and variable selection. Multiple simulation studies demonstrate significant advantages in computing, predictive modeling, and selection relative to existing alternatives.

Roth (1996) proved that any form of marginal inference with probabilistic graphical models (e.g. Bayesian Networks) will at least be NP-hard. Introduced and extensively investigated in the past decade, the neural probabilistic circuits known as sum-product network (SPN) offers linear time complexity. On another note, research around neural causal models (NCM) recently gained traction, demanding a tighter integration of causality for machine learning. To this end, we present a theoretical investigation of if, when, how and under what cost tractability occurs for different NCM. We prove that SPN-based causal inference is generally tractable, opposed to standard MLP-based NCM. We further introduce a new tractable NCM-class that is efficient in inference and fully expressive in terms of Pearl's Causal Hierarchy. Our comparative empirical illustration on simulations and standard benchmarks validates our theoretical proofs.

We propose a Bayesian approach for both medical inquiry and disease inference, the two major phases in differential diagnosis. Unlike previous work that simulates data from given probabilities and uses ML algorithms on them, we directly use the Quick Medical Reference (QMR) belief network, and apply Bayesian inference in the inference phase and Bayesian experimental design in the inquiry phase. Moreover, we improve the inquiry phase by extending the Bayesian experimental design framework from one-step search to multi-step search. Our approach has some practical advantages as it is interpretable, free of costly training, and able to adapt to new changes without any additional effort. Our experiments show that our approach achieves new state-of-the-art results on two simulated datasets, SymCAT and HPO, and competitive results on two diagnosis dialogue datasets, Muzhi and Dxy.