lower values are more preferable. Deep Learning algorithms aim to learn feature hierarchies with features at higher levels in the hierarchy formed by the composition of lower level features. to parameters \(\theta\) of the generator also! Then $$H_l(x) = [z \le l] F_l(x) + x$$, Thus we have $$p(y|x,z) = \text{Categorical}(y \mid \pi(x, z))$$ where \(\pi(x, z)\) is a residual network with \(z\) that controls when to stop processing the \(x\), We chose the prior on \(z\) s.t. Video and slides of NeurIPS tutorial on Efficient Processing of Deep Neural Networks: from Algorithms to Hardware Architectures available here. 8. We have a continuous density \(q(\theta_i | \mu_i(\Lambda), \sigma_i^2(\Lambda))\) and would like to compute the gradient of $$ \mathbb{E}_{q(\theta|\Lambda)} \log \frac{p(\mathcal{D}|\theta) p(\theta)}{q(\theta|\Lambda)} $$, The inner part – expected gradients of \(\log \frac{p(\mathcal{D}|\theta) p(\theta)}{q(\theta|\Lambda)} \), Sampling part – gradients through samples \( \theta \sim q(\theta|\Lambda) \), The objective then becomes $$ \mathbb{E}_{\varepsilon \sim \mathcal{N}(0, 1)} \log \tfrac{p(\mathcal{D}, \mu + \varepsilon \sigma)}{q(\mu + \varepsilon \sigma | \Lambda)} $$, The objective then becomes $$ \mathbb{E}_{\varepsilon \sim \mathcal{N}(0, 1)} \left[\sum_{n=1}^N \log p(y_n | \theta=\mu(\Lambda) + \varepsilon \sigma(\Lambda)) \right] - \text{KL}(q(\theta|\Lambda) || p(\theta)) $$, Training a neural network with special kind of noise upon weights, The magnitude of the noise is encouraged to increase, Zeroes out unnecessary weights completely, Essentially, training a whole ensemble of neural networks, Actually using the ensemble is costly: \(k\) times slow for an ensemble of \(k\) models, Single network (single-sample ensemble) also work. \(\mathbb{E} \hat{g} = \nabla_\Lambda \mathcal{L}(\Lambda) \), Problem: We can't just take \(\hat{g} = \nabla_\Lambda \log \frac{p(\mathcal{D}, \theta)}{q(\theta | \Lambda)} \) as the samples themselves depend on \(\Lambda\) through \(q(\theta|\Lambda)\), Remember the expectation is just an integral, and apply the log-derivative trick $$ \nabla_\Lambda q(\theta | \Lambda) = q(\theta | \Lambda) \nabla_\Lambda \log q(\theta|\Lambda) $$ $$ \nabla_\Lambda \mathcal{L}(\Lambda) = \int q(\theta|\Lambda) \log \frac{p(\mathcal{D}, \theta)}{q(\theta | \Lambda)} \nabla_\Lambda \log q(\theta | \Lambda) d\theta = \mathbb{E}_{q(\theta|\Lambda)} \log \frac{p(\mathcal{D}, \theta)}{q(\theta|\Lambda)} \nabla \log q(\theta | \Lambda) $$, Though general, this gradient estimator has too much variance in practice, We assume the data is generated using some (partially known) classifier \(\pi_{\theta}\): $$ p(y \mid x, \theta) = \text{Cat}(y | \pi_\theta(x)) \quad\quad \theta \sim p(\theta) $$, True posterior is intractable $$ p(\theta \mid \mathcal{D}) \propto p(\theta) \prod_{n=1}^N p(y_n \mid x_n, \pi_\theta) $$, Approximate it using \(q(\theta | \Lambda)\): $$ \Lambda_* = \text{argmax} \; \mathbb{E}_{q(\theta | \Lambda)} \left[\sum_{n=1}^N \log p(y_n | x_n, \theta) - \text{KL}(q(\theta | \Lambda) || p(\theta))\right] $$, Essentially, instead of learning a single neural network that would solve the problem, we, \(p(\theta)\) encodes our preferences on which networks we'd like to see, Let \(q(\theta_i | \Lambda)\) be s.t. The course covers the basics of Deep Learning… The Deep Learning Lecture Series 2020 is a collaboration between DeepMind and the UCL Centre for Artificial Intelligence. Deep Learning is one of the most highly sought after skills in tech. If you want to break into Artificial intelligence (AI), this Specialization will help you. The Course “Deep Learning” systems, typified by deep neural networks, are increasingly taking over all AI tasks, ranging from language understanding, and speech and image recognition, to machine translation, planning, and even game playing and autonomous driving. Lets equip the network with a mechanism to decide when to stop processing and prefer networks that stop early, Let \(z\) indicate the number of layers to use. To find out more, please visit MIT Professional Education. Note: press “P” to display the presenter’s notes that include some comments and Description. "Backpropagation applied to handwritten zip code recognition." Nature 2015 Machine Learning: An Overview: The slides presentintroduction to machine learningalong with some of the following: 1. additional references. "Learning representations by back-propagating errors." Book Exercises External Links Lectures. The course is Berkeley’s current offering of deep learning. Deep Learning Handbook. 2014 Lecture 2 … Inria. lectures-labs maintained by m2dsupsdlclass, Convolutional Neural Networks for Image Classification, Deep Learning for Object Detection and Image Segmentation, Sequence to sequence, attention and memory, Expressivity, Optimization and Generalization, Imbalanced classification and metric learning, Unsupervised Deep Learning and Generative models, Demo: Object Detection with pretrained RetinaNet with Keras, Backpropagation in Neural Networks using Numpy, Neural Recommender Systems with Explicit Feedback, Neural Recommender Systems with Implicit Feedback and the Triplet Loss, Fine Tuning a pretrained ConvNet with Keras (GPU required), Bonus: Convolution and ConvNets with TensorFlow, ConvNets for Classification and Localization, Character Level Language Model (GPU required), Transformers (BERT fine-tuning): Joint Intent Classification and Slot Filling, Translation of Numeric Phrases with Seq2Seq, Stochastic Optimization Landscape in Pytorch. Different types of learning (supervised, unsupervised, reinforcement) 2. @article{zhang2019pathologist, title={Pathologist-level interpretable whole-slide cancer diagnosis with deep learning}, author={Zhang, Zizhao and Chen, Pingjun and McGough, Mason and Xing, Fuyong and Wang, Chunbao and Bui, Marilyn and Xie, Yuanpu and Sapkota, Manish and Cui, Lei and Dhillon, Jasreman and others}, journal={Nature Machine Intelligence}, volume={1}, number={5}, … However, while deep learning has proven itself to be extremely powerful, most of today’s most successful deep learning systems suffer from a number of important limitations, ranging from the requirement for enormous training data sets to lack of interpretability to vulnerability to … We want to make predictions about some \( x \), $$ p(X = k) = \pi_k \Leftrightarrow p(x) = \prod_{k=1}^K \pi_k^{[x = k]} $$, Variational Dropout Sparsifies Deep Neural Networks, D. Molchanov, A. Ashukha, D. Vetrov, ICML 2017. All the code in this repository is made available under the MIT license we don't need the exact true posterior $$ \text{KL}(q(\theta | \Lambda) || p(\theta | \mathcal{D})) = \log p(\mathcal{D}) - \mathbb{E}_{q(\theta | \Lambda)} \log \frac{p(\mathcal{D}, \theta)}{q(\theta | \Lambda)} $$, Hence we seek parameters \(\Lambda_*\) maximizing the following objective (the ELBO) $$ \Lambda_* = \text{argmax}_\Lambda \left[ \mathbb{E}_{q(\theta | \Lambda)} \log \frac{p(\mathcal{D}, \theta)}{q(\theta|\Lambda)} = \mathbb{E}_{q(\theta|\Lambda)} \log p(\mathcal{D}|\theta) - \text{KL}(q(\theta|\Lambda)||p(\theta)) \right]$$, We can't compute this quantity analytically either, but can sample from \(q\) to get Monte Carlo estimates of the approximate posterior predictive distribution: $$ q(y \mid x, \mathcal{D}) \approx \hat{q}(y|x, \mathcal{D}) = \frac{1}{M} \sum_{m=1}^M p(y \mid x, \theta^m), \quad\quad \theta^m \sim q(\theta \mid \Lambda_*) $$, Recall the objective for variational inference $$ \mathcal{L}(\Lambda_*) = \mathbb{E}_{q(\theta | \Lambda)} \log \frac{p(\mathcal{D}, \theta)}{q(\theta|\Lambda)} \to \max_{\Lambda} $$, We'll be using well-known optimization method, We need (stochastic) gradient \(\hat{g}\) of \(\mathcal{L}(\Lambda)\) s.t. In this study, we used two deep-learning algorithms based … Predicting survival after hepatocellular carcinoma resection using deep-learning on histological slides Hepatology. Lecture slides Basic information about deep learning Cheat sheet – stuff that everyone needs to know Useful links Grading Plan your visit Visit previous iteration of Stats385 (2017) This page was generated by … CNNs are the current state-of-the-art architecture for medical image analysis. Cognitive modeling 5.3 (1988): 1. deep learning is driving significant advancements across industries, enterprises, and our everyday lives. Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. Unsupervised Deep Learning Tutorial – Part 1 Alex Graves NeurIPS, 3 December 2018 ... Slide: Irina Higgins, Loïc Matthey. Gradient-based optimization in discrete models is hard, Invoke the Central Limit Theorem and turn the model into a continuous one, Consider a model with continuous noise on weights $$ q(\theta_i | \Lambda) = \mathcal{N}(\theta_i | \mu_i(\Lambda), \alpha_i(\Lambda) \mu^2_i(\Lambda)) $$, Neural Networks have lots of parameters, surely there's some redundancy in them, Let's take a prior \(p(\theta)\) that would encourage large \(\alpha\), Large \(\alpha_i\) would imply that weight \(\theta_i\) is unbounded noise that corrupts predictions, Such weights won't be doing anything useful, hence it should be zeroed out by putting \(\mu_i(\Lambda) = 0\), Thus the weight \(\theta_i\) would effectively turn into a deterministic 0. Olivier Grisel, software engineer at What is Deep Learning? This course is being taught at as part of Master Datascience Paris The Deep Learning Specialization was created and is taught by Dr. Andrew Ng, a global leader in AI and co-founder of Coursera. We thank the Orange-Keyrus-Thalès chair for supporting this class. However, many found the accompanying video lectures, slides, and exercises not pedagogic enough for a fresh starter. • LeCun, Yann, et al. 10/18/2019 ∙ by Neofytos Dimitriou, et al. Bayesian methods can Impose useful priors on Neural Networks helping discover solutions of special form; Provide better predictions; Provide Neural Networks with uncertainty estimates (uncovered) Neural Networks help us make more efficient Bayesian inference; Uses a lot of math; Active area of research The Deep Learning Handbook is a project in progress to help study the Deep Learning book by Goodfellow et al.. Goodfellow's masterpiece is a vibrant and precious resource to introduce the booming topic of deep learning. Download Deep Learning PowerPoint templates (ppt) and Google Slides themes to create awesome presentations. To get around the costly computations associated with large models and data, the … Its uncertainty quantified by the, This requires us to know the posterior distribution on model parameters \(p(\theta \mid \mathcal{D})\) which we obtain using the Bayes' rule, Suppose the model \(y \sim \mathcal{N}(\theta^T x, \sigma^2)\), with \( \theta \sim \mathcal{N}(\mu_0, \sigma_0^2 I) \), Suppose we observed some data from this model \( \mathcal{D} = \{(x_n, y_n)\}_{n=1}^N \) (generated using the same \( \theta^* \)), We don't know the optimal \(\theta\), but the more data we observe, Posterior predictive would also be Gaussian $$ p(y|x, \mathcal{D}) = \mathcal{N}(y \mid \mu_N^T x, \sigma_N^2) $$, Suppose we observe a sequence of coin flips \((x_1, ..., x_N, ...)\), but don't know whether the coin is fair $$ x \sim \text{Bern}(\pi), \quad \pi \sim U(0, 1) $$, First, we infer posterior distribution on a hidden parameter \(\pi\) having observed \(x_{

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