Machine Learning Basics

Deep Learning

Contents Websiteviii Acknowledgmentsix Notationxiii 1 Introduction1 1.1 WhoShouldReadThisBook?. . . . . . . . . . . . . . . . . . . . 8 1.2 ...

  Learning, Deep, Deep learning

Introduction - Deep Learning

human time and e ffort; it can take decades for an entire community of researchers. The quintessential example of a representation learning algorithm is the au-toencoder. An autoencoder is the combination of an encoder function that converts the input data into a different representation, and a decoder function

  Human, Learning, Representation, Representation learning

Autoencoders - Deep Learning

biologically plausible than back-propagation, but is rarely used for machine learning applications. x r h f g Figure 14.1: The general structure of an autoencoder, mapping an input x to an output (called reconstruction) r through an internal representation or code h. The autoencoder

  Propagation, Autoencoder

Regularization for Deep Learning

Lecture slides for Chapter 7 of Deep Learning www.deeplearningbook.org ... of an abstract, general, quadratic cost function. How do these effects relate to ... 14 1 19 2 23 3 7 7 7 7 5 = 2 6 6 6 6 4 3 1254 1 423 11 3 15 4 23 2 312303 54225 1 3 7 7 7 7 5 2 6 6 6 6 6 6 4 0 2 0 0 3 0 3 7 7 7 7 7 7 5 y 2 Rm B 2 Rm⇥n h 2 Rn (7.47)

  Lecture, Cost

Deep Learning

Bibliography Abadi,M.,Agarwal,A.,Barham,P.,Brevdo,E.,Chen,Z.,Citro,C.,Corrado,G.S.,Davis, A.,Dean,J.,Devin,M.,Ghemawat,S.,Goodfellow,I.,Harp,A.,Irving,G.,Isard,M.,

  Learning, Deep, Deep learning

QR Factorization and Singular Value Decomposition

SVD and the Pseudoinverse • A-1=(VT)-1 W-1 U-1 = V W-1 UT • This fails when some w i are 0 – It’s supposed to fail – singular matrix – Happens when rectangular A is rank deficient • Pseudoinverse: if w i=0, set 1/w i to 0 (!) – “Closest” matrix to inverse – Defined for all (even non-square, singular, etc.) matrices

  Pseudoinverse

MATLAB Commands and Functions - University of Minnesota

pinv Computes pseudoinverse of a matrix. rank Computes rank of a matrix. rref Computes reduced row echelon form. MATLAB Commands – 7 Cell Array Functions cell Creates cell array. celldisp Displays cell array. cellplot Displays graphical representation of cell array.

  Command, Matlab, Matlab commands, Pseudoinverse

The Lasso Problem and Uniqueness - Carnegie Mellon …

The Lasso Problem and Uniqueness Ryan J. Tibshirani Carnegie Mellon University Abstract The lasso is a popular tool for sparse linear regression, especially for problems in which the

  Problem, Sasol, Uniqueness, The lasso problem and uniqueness

High Dimensional Statistics - MIT Mathematics

Nov 05, 2019 · Notation Functions, sets, vectors [n] Set of integers [n] = f1;:::;ng Sd 1 Unit sphere in dimension d 1I() Indicator function jxj q ‘ q norm of xde ned by jxj q= P i jx ij q 1 q for q>0 jxj 0 ‘ 0 norm of xde ned to be the number of nonzero coordinates of x f(k) k-th derivative of f e j j-th vector of the canonical basis Ac complement of set A conv(S) Convex hull of set S.

An introduction to optimization on smooth manifolds - EPFL

M† Moore–Penrose pseudoinverse of matrix M I d Identity matrix of size d I Subset of R (often open with 0 ∈I) or identity matrix Id Identity operator |a| Modulus of a∈C (absolute value if a∈R) |A| Cardinality of a set A E,E′,F Linear spaces, often with a Euclidean structure M,M′,M,N Smooth manifolds, often with a Riemannian structure

  Pseudoinverse

LSQR: An Algorithm for Sparse Linear Equations and …

pseudoinverse of A. The relative precision of floating-point arithmetic is e, the smallest machine-representable number such that 1 + e > 1. 2. MOTIVATION VIA THE LANCZOS PROCESS In this section we review the symmetric Lanczos process [13] and its use in solving symmetric linear equations Bx = b.

  Linear, Equations, Algorithm, Arsesp, Pseudoinverse, Algorithm for sparse linear equations and