Bayesian optimization. Part 2

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Do curso por National Research University Higher School of Economics

Addressing Large Hadron Collider Challenges by Machine Learning

8 classificações

National Research University Higher School of Economics

Addressing Large Hadron Collider Challenges by Machine Learning

8 classificações

Curso 7 de 7 em Specialization Advanced Machine Learning

The Large Hadron Collider (LHC) is the largest data generation machine for the time being. It doesn’t produce the big data, the data is gigantic. Just one of the four experiments generates thousands gigabytes per second. The intensity of data flow is only going to be increased over the time. So the data processing techniques have to be quite sophisticated and unique. In this course we’ll introduce students into the main concepts of the Physics behind those data flow so the main puzzles of the Universe Physicists are seeking answers for will be much more transparent. Of course we will scrutinize the major stages of the data processing pipelines, and focus on the role of the Machine Learning techniques for such tasks as track pattern recognition, particle identification, online real-time processing (triggers) and search for very rare decays. The assignments of this course will give you opportunity to apply your skills in the search for the New Physics using advanced data analysis techniques. Upon the completion of the course you will understand both the principles of the Experimental Physics and Machine Learning much better.

Na lição

Detector optimization

This module covers several cases of detector design optimization in high energy physics experiments using Bayesian optimization with Gaussian processes.

Detector optimization7:05

Normal distribution3:37

Gaussian processes for regression4:26

Bayesian optimization. Part 14:36

Bayesian optimization. Part 25:09

Optimization examples3:29

Conheça os instrutores

Andrei Ustyuzhanin
Head of Laboratory for Methods of Big Data Analysis
HSE Faculty of Computer Science
Mikhail Hushchyn
Researcher at Laboratory for Methods of Big Data Analysis
HSE Faculty of Computer Science

[MUSIC]

In this video, we will talk about the exploration-exploitation trade-off of

the Bayesian optimization.

But firstly, let me remind you key points about the Bayesian optimization.

So the Bayesian optimization is a method of finding the optimum

of expensive cost functions.

This cost function is also called objective function and denoted as f.

It supposed that calculation of f at one point is expensive.

And the derivatives of these functions are unknown.

The goal of Bayesian optimization is to find the optimum of the objective function

using as small number of the function calculations as possible.

The optimization algorithm is follow.

And the first step finds the objective function approximation using previously

calculated values, and solving the regression problem.

Then using the approximation find optimum point of an acquisition function.

Then, after that, sample the objective function in this new point,

and repeat all the steps.

There are variety of acquisition functions, and one of them used in this

video is Lower Confidence Bound for the object function minimization.

The Bayesian optimization with Gaussian processes allows to balance between

exploration and exploitation of the objective function.

Exploration is when you choose a point

with high variance at each iteration of the optimization.

And exploitation, it's when you choose a point with high or

low mean at each iteration of the optimization.

Adjustable parameters of the acquisition functions

provide trade-off between exploration and exploitation.

To study the exploration-exploitation properties of the Bayesian optimization,

consider the following objective function f.

The goal in this example is to find its minimum.

Let's start the optimization from three observations.

Firstly, consider the exploitation property.

Exploitation can be achieved with a small values of k

parameter in lower confidence bound function.

After ten iterations, we have almost all observations in the local minimum.

And there are just few observations in other regions of the function.

After 20 iterations, we again have almost all observations in the minima regions,

and there are just few observations in other regions.

This is the exploitation property of the Bayesian optimization with Gaussian

processes.

The key features of the exploitation are follow.

So exploitation takes a new point at each iteration

close to found optimum of the objective function.

There is no guarantee that this optimum is global.

Other regions of the objective function are not explored, and

it needs less iterations that for exploration to find the optimum.

Now consider the exploration property of the Bayesian optimization.

Exploration can be achieved with large values of k

in lower confidence bound function.

In the exploration case all observations are distributed through the whole region.

The target function is explored during the Bayesian optimization.

After twenty iterations,

all observations are again distributed through the whole region.

And this is exploration property of the Bayesian optimization with

Gaussian processes.

So during the exploration, it's taken a new point at each iteration

where the variance of the approximation of the objective function is large.

All regions of the objective functions are explored.

It's more likely that the found optimum is global.

And it needs more iterations than for exploitation to find the optimum.

Finally, we have learned the Bayesian optimization.

Bayesian optimization is a method of finding the optimum of expensive cost

functions.

We know how it works and how to use the exploration-exploitation trade-off during the optimization.

In high energy physics, Bayesian optimization with Gaussian processes

can be used for detector design optimization.

In the next video,

we consider two examples of the optimization in high energy physics.

[MUSIC]

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