Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution, which can typically be written as a product of its marginals -- thus drawing a connection with the field of nonlinear independent component analysis. Deep density models have been widely used for this task, but their maximum likelihood based training requires estimating the log-determinant of the Jacobian and is computationally expensive, thus imposing a trade-off between computation and expressive power. In this work, we propose a new approach for exact training of such neural networks. Based on relative gradients, we exploit the matrix structure of neural network parameters to compute updates efficiently even in high-dimensional spaces; the computational cost of the training is quadratic in the input size, in contrast with the cubic scaling of naive approaches. This allows fast training with objective functions involving the log-determinant of the Jacobian, without imposing constraints on its structure, in stark contrast to autoregressive normalizing flows.

Summary and Contributions: Quite a bit of recent research on deep density estimation under the normalizing flows umbrella has focused on efficiently computing (a restricted form of) the Jacobian term that appears in the objective. Such models operate with a set of transformations where the computation of this term is easy. While arbitrary distributions can be learned by such methods, the features that are learned are quite skewered which can prevent learning a proper disentangled representation. This paper presents a conceptually simple method to optimize for exact maximum likelihood in such models. In particular, the authors consider a transform from the observed to the latent space which is parameterized by fully connected networks with the only constraint that the weight matrices are invertible. Since the parameters of the transformation are matrices, the authors use properties of Riemannian geometry of matrix spaces to derive updates in terms of the relative gradient.

The focus of the work is deep density estimation (also called normalizing flows). Particularly, the authors focus on the generative model x f(s) as defined in (1) where the observation (x) is described as the invertible non-linear function (f) of a latent variable (s). They take a maximum-likelihood perspective (2) where g_{\theta}, the approximation of the inverse of f, is the composition of g_1 \sigma_1(W_1 \cdot), ..., g_L \sigma_L(W_L \cdot) invertible and differentiable component functions. They propose to use the relative gradient method to optimize \theta to speed up computations. Deep density estimation is an important problem in machine learning.

Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution, which can typically be written as a product of its marginals -- thus drawing a connection with the field of nonlinear independent component analysis. Deep density models have been widely used for this task, but their maximum likelihood based training requires estimating the log-determinant of the Jacobian and is computationally expensive, thus imposing a trade-off between computation and expressive power. In this work, we propose a new approach for exact training of such neural networks. Based on relative gradients, we exploit the matrix structure of neural network parameters to compute updates efficiently even in high-dimensional spaces; the computational cost of the training is quadratic in the input size, in contrast with the cubic scaling of naive approaches.

We present a framework for cloud characterization that leverages modern unsupervised deep learning technologies. While previous neural network-based cloud classification models have used supervised learning methods, unsupervised learning allows us to avoid restricting the model to artificial categories based on historical cloud classification schemes and enables the discovery of novel, more detailed classifications. Our framework learns cloud features directly from radiance data produced by NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) satellite instrument, deriving cloud characteristics from millions of images without relying on pre-defined cloud types during the training process. We present preliminary results showing that our method extracts physically relevant information from radiance data and produces meaningful cloud classes.

Free Coupon Discount - Ensemble Machine Learning in Python: Random Forest, AdaBoost, Ensemble Methods: Boosting, Bagging, Boostrap, and Statistical Machine Learning for Data Science in Python Created by Lazy Programmer Inc. Students also bought Unsupervised Deep Learning in Python Machine Learning and AI: Support Vector Machines in Python Data Science: Natural Language Processing (NLP) in Python Deep Learning: Advanced Computer Vision (GANs, SSD, More!) Deep Learning Prerequisites: Linear Regression in Python Preview this Udemy Course GET COUPON CODE Description In recent years, we've seen a resurgence in AI, or artificial intelligence, and machine learning. Machine learning has led to some amazing results, like being able to analyze medical images and predict diseases on-par with human experts. Google's AlphaGo program was able to beat a world champion in the strategy game go using deep reinforcement learning. Machine learning is even being used to program self driving cars, which is going to change the automotive industry forever. Imagine a world with drastically reduced car accidents, simply by removing the element of human error.

Created by Lazy Programmer Inc. English [Auto-generated] Created by Lazy Programmer Inc. This course is the next logical step in my deep learning, data science, and machine learning series. I've done a lot of courses about deep learning, and I just released a course about unsupervised learning, where I talked about clustering and density estimation. So what do you get when you put these 2 together? In these course we'll start with some very basic stuff - principal components analysis (PCA), and a popular nonlinear dimensionality reduction technique known as t-SNE (t-distributed stochastic neighbor embedding).

Free Coupon Discount - Theano / Tensorflow: Autoencoders, Restricted Boltzmann Machines, Deep Neural Networks, t-SNE and PCA Created by Lazy Programmer Inc. Students also bought Artificial Intelligence: Reinforcement Learning in Python Advanced AI: Deep Reinforcement Learning in Python Machine Learning A-Z: Hands-On Python & R In Data Science Learn Python Programming Masterclass Complete Python Developer in 2020: Zero to Mastery Preview this Udemy Course GET COUPON CODE Description This course is the next logical step in my deep learning, data science, and machine learning series. I've done a lot of courses about deep learning, and I just released a course about unsupervised learning, where I talked about clustering and density estimation. So what do you get when you put these 2 together? In these course we'll start with some very basic stuff - principal components analysis (PCA), and a popular nonlinear dimensionality reduction technique known as t-SNE (t-distributed stochastic neighbor embedding). Next, we'll look at a special type of unsupervised neural network called the autoencoder.

This course is the next logical step in my deep learning, data science, and machine learning series. I've done a lot of courses about deep learning, and I just released a course about unsupervised learning, where I talked about clustering and density estimation. So what do you get when you put these 2 together? In these course we'll start with some very basic stuff - principal components analysis (PCA), and a popular nonlinear dimensionality reduction technique known as t-SNE (t-distributed stochastic neighbor embedding). Next, we'll look at a special type of unsupervised neural network called the autoencoder.

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