Gradient Descent

Sep 03, 2021

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Gradient Descent is an optimization algorithm used for minimizing the cost function in various machine learning algorithms. It is basically used for updating the parameters of the learning model.

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Gradient Descent

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Online convex optimization Gradient descent without a gradient

Online convex optimization Gradient descent without a gradient. Abie Flaxman CMU Adam Tauman Kalai TTI Brendan McMahan CMU. Goal: find x f(x) ¸ max z 2 S f(z) – . High-dimensional. } . Standard convex optimization. Convex feasible set S ½ < d Concave function f : S ! <.

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A note about gradient descent: Consider the function f(x)=(x-x 0 ) 2 Its derivative is: By gradient descent

A note about gradient descent: Consider the function f(x)=(x-x 0 ) 2 Its derivative is: By gradient descent (If f(x) is more complex we usually cannot solve explicitly the convergence to the fixed point s .). + -. x 0. Solving the differential equation:.

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Blind online optimization Gradient descent without a gradient

Blind online optimization Gradient descent without a gradient. Abie Flaxman CMU Adam Tauman Kalai TTI Brendan McMahan CMU. Goal: find x f(x) ¸ max z 2 S f(z) –  = f(x*) - . } . R d. Standard convex optimization. Convex feasible set S ½ < d Concave function f : S ! <. x*.

690 views • 28 slides

Semi-Stochastic Gradient Descent Methods

Semi-Stochastic Gradient Descent Methods. Jakub Kone čný (joint work with Peter Richt árik ) University of Edinburgh. Introduction. Large scale problem setting. Problems are often structured Frequently arising in machine learning. is BIG. Structure – sum of functions. Examples.

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Semi-Stochastic Gradient Descent Methods

SIAM Annual Meeting, Chicago July 7, 2014. Semi-Stochastic Gradient Descent Methods. Jakub Kone čný (joint work with Peter Richt árik ) University of Edinburgh. Introduction. Large scale problem setting. Problems are often structured Frequently arising in machine learning. is BIG.

580 views • 30 slides

Gradient descent

Gradient descent. David Kauchak CS 451 – Fall 2013. Admin. Assignment 5. Math background. Linear models. A strong high-bias assumption is linear separability : in 2 dimensions, can separate classes by a line in higher dimensions, need hyperplanes

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Descent

Luke 9 – Entering the Fray. Descent.

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Objectives: Linear Discriminant Functions Gradient Descent Nonseparable Data

LECTURE 20 : LINEAR DISCRIMINANT FUNCTIONS. Objectives: Linear Discriminant Functions Gradient Descent Nonseparable Data Resources: SM: Gradient Descent JD: Optimization Wiki: Stochastic Gradient Descent MJ: Linear Programming. Discriminant Functions.

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Gradient Descent with Numpy

Gradient Descent with Numpy. COMP 4332 Tutorial 3 Feb 25. Outline. Main idea of Gradient Descent 1 dimension example 2 dimension example Useful tools in Scipy Simply ploting. Main idea of Gradient Descent. Goal: optimize a function

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Gradient Descent (Ascent)

Gradient Descent (Ascent). By Eni Sumarminingsih , SSi , MM. Gradien t descent (ascent) adalah algoritma optimasi orde pertama.

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Better Data Assimilation through Gradient Descent

London Mathematical Society - EPSRC Durham Symposium Mathematics of Data Assimilation. Better Data Assimilation through Gradient Descent. Leonard A. Smith, Kevin Judd and Hailiang Du Centre for the Analysis of Time Series London School of Economics. Outline. Perfect model scenario (PMS)

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Stochastic Gradient Descent and Tree Parameterizations in SLAM

Stochastic Gradient Descent and Tree Parameterizations in SLAM. G. Grisetti. Autonomous Intelligent Systems Lab Department of Computer Science, University of Freiburg, Germany. Special thanks to E. Olson, G.D. Tipaldi, S. Grzonka, C. Stachniss, D. Rizzini, B. Steder, W. Burgard, ….

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Gradient Descent Rule Tuning

Gradient Descent Rule Tuning. See pp. 207-210 in text book. Rules. Consider a rule base with M rules, r th rule has the form IF x 1 is T r,1 AND … AND x n is T r,n THEN y is y r (or y is y r + other stuff ) TSK fuzzy system has mathematical form. Membership function parameters

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Gradient descent assimilation for the point vortex model

Gradient descent assimilation for the point vortex model. Emma Suckling, Leonard A. Smith and Hailiang Du. Centre for the Analysis of Time Series, London School of Economics www2.lse.ac.uk/CATS. International Conference on Data Assimilation, Bangalore, 14 July 2011. Outline. Lagrangian data

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Efficient Logistic Regression with Stochastic Gradient Descent: The Continuing Saga

Efficient Logistic Regression with Stochastic Gradient Descent: The Continuing Saga. William Cohen. Outline. SGD review The “hash trick” the idea an experiment Other randomized algorithms Bloom filters Locality sensitive hashing. Learning as optimization: general procedure for SGD.

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Efficient Logistic Regression with Stochastic Gradient Descent

Efficient Logistic Regression with Stochastic Gradient Descent. William Cohen. Admin. Phrase assignment extension We forgot about discarding phrases with stop words Aside: why do stop words hurt performance? How many map-reduce assignments does it take to screw in a lightbulb ? ?

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The Gradient Descent Algorithm

The Gradient Descent Algorithm. Initialize all weights to small random values. REPEAT until done 1- For each weight w ij set 2- For each data point ( x, t )p set input units to x compute value of output units For each weight w ij set

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Efficient Logistic Regression with Stochastic Gradient Descent – part 2

Efficient Logistic Regression with Stochastic Gradient Descent – part 2. William Cohen. Learning as optimization: warmup. Goal: Learn the parameter θ of a binomial Dataset: D={x 1 ,…, x n }, x i is 0 or 1, k of them are 1. = 0. θ = 0. θ = 1. k- kθ – nθ + kθ = 0 nθ = k

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Efficient Logistic Regression with Stochastic Gradient Descent

Efficient Logistic Regression with Stochastic Gradient Descent. William Cohen. Outline. Logistic regression and SGD Learning as optimization Logistic regression: a linear classifier optimizing P( y| x ) Stochastic gradient descent “streaming optimization” for ML problems

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Gradient Descent

Gradient Descent. Slides adapted from David Kauchak , Michael T. Brannick , Ethem Alpaydin , and Yaser Abu-Mostafa. Linear models. A strong high-bias assumption is linear separability : in 2 dimensions, can separate classes by a line in higher dimensions, need hyperplanes

494 views • 35 slides

Better Data Assimilation through Gradient Descent

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ECE471-571 – Pattern Recognition Lecture 14 – Gradient Descent

ECE471-571 – Pattern Recognition Lecture 14 – Gradient Descent. Hairong Qi, Gonzalez Family Professor Electrical Engineering and Computer Science University of Tennessee, Knoxville http://www.eecs.utk.edu/faculty/qi Email: hqi@utk.edu. Pattern Classification. Statistical Approach.

148 views • 10 slides

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