The Case for Bayesian Deep Learning Andrew Gordon Wilson andrewgw@cims.nyu.edu Courant Institute of Mathematical Sciences Center for Data Science Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priors Uncertainty Estimations by Softplus normalization in Bayesian Convolutional Neural Networks with Variational Inference Other methods [12, 16, 28] have been proposed to approximate the posterior distributions or estimate model uncertainty of a neural network. Deep Bayesian Multi-Target Learning for Recommender Systems Qi Wang 1, Zhihui Ji , Huasheng Liu1 and Binqiang Zhao1 1Alibaba Group fwq140362, jiqi.jzh, fangkong.lhs, binqiang.zhaog@alibaba-inc.com Abstract With the increasing variety of services that e- 4th workshop on Bayesian Deep Learning (NeurIPS 2019), Vancouver, Canada. = 𝐌 2 Seismic Bayesian evidential learning: Estimation and uncertainty quantification of sub-resolution reservoir properties ... Download file PDF Read file. Third workshop on Bayesian Deep Learning (NeurIPS 2018), Montréal, Canada. BKT models a learner’s latent knowledge state as a set of binary variables, each of which represents understanding or non-understanding of … 4. We can transform dropout’s noise from the feature space to the parameter space as follows. We introduce two 1 Towards Bayesian Deep Learning: A Survey Hao Wang, Dit-Yan Yeung Hong Kong University of Science and Technology fhwangaz,dyyeungg@cse.ust.hk Abstract—While perception tasks such as … deep learning tools as Bayesian models – without chang-ing either the models or the optimisation. We cast the problem of learning the structure of a deep neural network as a problem of learning the structure of a deep (discriminative) probabilistic graphical model, G dis. Bayesian deep learning is grounded on learning a probability distribution for each parameter. Here we focus on a general approach by using the reparameterization gradient estimator. Non-Linearities: Bayesian Methods versus Deep Learning Ozlem Tugfe Demir,¨ Member, IEEE, Emil Bjo¨rnson, Senior Member, IEEE This paper considers the joint impact of non-linear hardware impairments at the base station (BS) and user equipments (UEs) on "Uncertainty in deep learning." | Neal, Bayesian Learning for Neural Networks In the 90s, Radford Neal showed that under certain assumptions, an in nitely wide BNN approximates a Gaussian process. 2. et al., 2005, Liang, 2010], naturally fits to train the adaptive hierarchical Bayesian model. However, ‘14): -approximate likelihood of latent variable model with varia8onal lower bound I will attempt to address some of the common concerns of this approach, and discuss the pros and cons of Bayesian modeling, and briefly discuss the relation to non-Bayesian machine learning. Taking inspiration from these works, in this paper we primarily focus on exploring the self-training algorithm in combination with modern Bayesian deep learning methods and leverage predictive uncertainty estimates for self-labelling of high-dimensional data. In recent years, Bayesian deep learning has emerged as a unified probabilistic framework to tightly integrate deep learning and Bayesian models. image data [2] and analysing deep transfer learning [11, 12] with good levels of success. Jähnichen et al., 2018; Wenzel et al., 2018). The Case for Bayesian Deep Learning Andrew Gordon Wilson andrewgw@cims.nyu.edu Courant Institute of Mathematical Sciences Center for Data Science New York University December 30, 2019 Abstract The key distinguishing property of a Bayesian approach is marginalization in-stead of optimization, not the prior, or Bayes rule. However, Bayesian inference is espe- First, active learning (AL) methods Take-Home Point 2. This score corresponds to log-likelihood of the observed data with Dirac approximation of the prior on the latent variable. The emerging research area of Bayesian Deep Learning seeks to combine the benefits of modern deep learning methods (scalable gradient-based training of flexible neural networks for regression and classification) with the benefits of modern Bayesian statistical methods to estimate probabilities and make decisions under uncertainty. I Neural nets are much less mysterious when viewed through the lens of Bayesian methods provide a natural probabilistic representation of uncertainty in deep learning [e.g., 6, 31, 9], and previously had been a gold standard for inference with neural networks [49]. The +1 is introduced here to account for Roger Grosse and Jimmy Ba CSC421/2516 Lecture 19: Bayesian Neural Nets 12/22 Hence we propose the use of Bayesian Deep Learning (BDL). Deep learning poses several difficulties when used in an active learn-ing setting. Outline. While many Bayesian models exist, deep learning models obtain state-of-the-art perception of fine details and complex relationships[Kendall and Gal, 2017]. Probabilistic Deep Learning: With Python, Keras and TensorFlow Probability is a hands-on guide to the principles that support neural networks. Bayesian Deep Learning Why? University of Cambridge (2016). Start with a prior on the weights . Work carried out during an internship at Amazon, Cambridge. Since the number of weights is very large inference on them is impractical. The network has Llayers, with V lhidden units in layer l, and W= fW lgL l=1 is the collection of V l (V l 1 + 1) weight matrices. Bayesian Deep Learning DNNs have been shown to excel at a wide variety of su-pervised machine learning problems, where the task is to predict a target value y ∈ Y given an input x ∈ X. Deep Bayesian Active Learning with Image Data Yarin Gal1 2 Riashat Islam 1Zoubin Ghahramani Abstract Even though active learning forms an important pillar of machine learning, deep learning tools are not prevalent within it. Modern Deep Learning through Bayesian Eyes Yarin Gal yg279@cam.ac.uk To keep things interesting, a photo or an equation in every slide! I A powerful framework for model construction and understanding generalization I Uncertainty representation (crucial for decision making) I Better point estimates I It was the most successful approach at the end of the second wave of neural networks (Neal, 1998). Deep Learning is nothing more than compositions of functions on matrices. Bayesian deep learning is a field at the intersection between deep learning and Bayesian probability theory. Demystify Deep Learning; Demystify Bayesian Deep Learning; Basically, explain the intuition clearly with minimal jargon. Third workshop on Bayesian Deep Learning (NeurIPS 2018), Montréal, Canada. It offers principled uncertainty estimates from deep learning architectures. Compression and computational efficiency in deep learning have become a problem of great significance. Course Overview. x f (x) x Normalizing flows In order to obtain a good approximation to the posterior it is crucial to use Bayesian Deep Learning (MLSS 2019) Yarin Gal University of Oxford yarin@cs.ox.ac.uk Unless speci ed otherwise, photos are either original work or taken from Wikimedia, under Creative Commons license Perform training to infer posterior on the weights 3. Decomposition of Uncertainty in Bayesian Deep Learning would only be given by the additive Gaussian observation noise n, which can only describe limited stochastic patterns. I will also provide a brief tutorial on probabilistic reasoning. This weights posterior is then used to derive a posterior pdf on any input state. As a result, the asymptotic property allows us to combine simulated annealing and/or parallel tempering to accelerate the non-convex learning. Bayesian deep learning [22] provides a natural solution, but it is computationally expensive and challenging to train and deploy as an online service. Right: Well-calibrated fit using proposed MF-DGP model. In this work, we argue that the most principled and effective way to attack this problem is by adopting a Bayesian point of view, where through sparsity inducing priors we prune large parts of the network. We show that the use of dropout (and its variants) in NNs can be inter-preted as a Bayesian approximation of a well known prob-Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning 2.1 Bayesian Knowledge Tracing Bayesian Knowledge Tracing (BKT) is the most popular approach for building temporal models of student learning. MF-DGP NARGP AR1 high-fidelity low-fidelity (a) Left: Overfitting in the NARGP model. In this paper, we propose a sparse Bayesian deep learning algorithm, SG-MCMC-SA, to adaptively 30 Bayesian Deep Learning 3.1 Advanced techniques in variational inference We start by reviewing recent advances in VI. This posterior is not tractable for a Bayesian NN, and we use variational inference to approximate it. The Bayesian paradigm has the potential to solve some of the core issues in modern deep learning, such as poor calibration, data inefficiency, and catastrophic forgetting. How would deep learning systems capture uncertainty? 18 • Dropout as one of the stochastic regularization techniques In Bayesian neural networks, the stochasticity comes from our uncertainty over the model parameters. The Bayesian Deep Learning Toolbox a broad one-slide overview Goal: represent distribuons with neural networks data everything else (CS 236 provides a thorough treatment) 15 Latent variable models + variaAonal inference (Kingma & Welling ‘13, Rezende et al. BDL is an exciting field lying at the forefront of research. Learn to improve network performance with the right distribution for different data types, and discover Bayesian variants that can state their own uncertainty to increase accuracy. graphics, and that Bayesian machine learning can provide powerful tools. That is, a graph of the form X H(m 1) H(0)!Y, where “ ” represent a sparse connectivity … Take-Home Point 1. In computer vision, the input space X often corresponds to the space of … (unless specified otherwise, photos are either original work or taken from Wikimedia, under Creative Commons license) Just in the last few years, similar results have been shown for deep BNNs. Bayesian Deep Learning Bayesian Deep learning does the inference on the weightsof the NN: 1. We are interested in the posterior over the weights given our observables X,Y: p ω♣X,Y . Bayesian methods provide a natural probabilistic representation of uncertainty in deep learning [e.g., 3, 24, 5], and previously had been a gold standard for inference with neural networks [38]. Gal, Yarin.