Fast Computation of Wasserstein Barycenters Marco Cuturi Graduate School of Informatics, Kyoto University Arnaud Doucet Department of Statistics, University of Oxford Abstract We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the […]
Recurrent Neural Networks CMPUT 366: Intelligent Systems P&M §10.0-10.2, 10.10 1. Recap 2. Unfolding Computations 3. Recurrent Neural Networks 4. Long Short-Term Memory Lecture Outline Recap: Convolutional Neural Networks Convolutional networks: Specialized architecture for images Number of parameters controlled by using convolutions and pooling operations instead of dense connections • • • CHAPTER 9.
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CMPUT 366 F20: Supervised Learning VI James Wright & Vadim Bulitko November 24, 2020 CMPUT 366 F20: Supervised Learning VI 1 Lecture Outline Convolutional Networks GBC 9.0-9.4 CMPUT 366 F20: Supervised Learning VI 2 Recap: Neural Networks x1 h1 x2 h2 Each unit’s inputs are outputs from previous layer’s units Single unit h: Inputs x,
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Problem 10.1 CS5487 Problem Set 10 Kernels Antoni Chan Department of Computer Science City University of Hong Kong Kernel functions Constructing kernels from kernels Suppose k1(x,z) and k2(x,z) are valid kernels. Prove the following kernels are also valid kernels: (a) kernel scaling: (b) sum: (c) product: (d) input scaling: (e) polynomial: (f) exponential: k(x, z)
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Problem 1.6 Multivariate Gaussian (a) The multivariate Gaussian distribution is N (x|μ, ⌃) = 1 exp ⇢ 1 (x μ)T ⌃1 (x μ) . 2 (S.158) CS5487 Problem Set Solutions – Tutorials (1-5) Antoni Chan Department of Computer Science City University of Hong Kong Tutorial Problems (1-5) (2⇡)d/2 |⌃|1/2 Assuming a diagonal covariance matrix, ⌃
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CPSC 320: Steps in Algorithm Design and Analysis Solutions* In this worksheet, you will practice ve useful steps for designing and analyzing algorithms, starting from a possibly vague problem statement. These steps will be useful throughout the class. They could also be useful when you nd yourself thinking on your feet in an interview situation.
Problem 5.1 CS5487 Problem Set 5 Non-parametric estimation and clustering Antoni Chan Department of Computer Science City University of Hong Kong Kernel density estimators Bias and variance of the kernel density estimator In this problem, we will derive the bias and variance of the kernel density estimator. Let X = {x1, · · · ,
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Problem 1.1 CS5487 Problem Set 1 Probability Theory and Linear Algebra Review Antoni Chan Department of Computer Science City University of Hong Kong Probability Theory Linear Transformation of a Random Variable Let x be a random variable on R, and a,b ∈ R. Let y = ax + b be the linear transformation of x.
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Problem 3.1 Gamma function Misc. Math (x) = Z 1 ux1eudu. 0 The gamma function is defined as CS5487 Problem Set 3 Bayesian Parameter Estimation Antoni Chan Department of Computer Science City University of Hong Kong Use integration by parts to prove the relation (x + 1) = x(x). Also show that (1) = 1.
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CS5487 Problem Set Solutions – Homework and Tutorials Antoni Chan Department of Computer Science City University of Hong Kong Important Note: These problem set solutions are meant to be a study aid for the final exam only. They should not be used as “model answers” to help do the problem set. The point of the
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