Surrogate Modeling and Optimization for Scientific Machine Learning

Surrogates.jl

A surrogate model is an approximation method that mimics the behavior of a computationally expensive simulation. In more mathematical terms: suppose we are attempting to optimize a function f(p), but each calculation of f is very expensive. It may be the case we need to solve a PDE for each point or use advanced numerical linear algebra machinery, which is usually costly. The idea is then to develop a surrogate model g which approximates f by training on previous data collected from evaluations of f. The construction of a surrogate model can be seen as a three-step process:

  1. Sample selection
  2. Construction of the surrogate model
  3. Surrogate optimization

ALL the currently available sampling methods:

  • Grid
  • Uniform
  • Sobol
  • Latin Hypercube
  • Low Discrepancy
  • Kronecker
  • Golden
  • Random

ALL the currently available surrogate models:

  • Kriging
  • Kriging using Stheno
  • Radial Basis
  • Wendland
  • Linear
  • Second Order Polynomial
  • Support Vector Machines (Wait for LIBSVM resolution)
  • Neural Networks
  • Random Forests
  • Lobachevsky
  • Inverse-distance
  • Polynomial expansions
  • Variable fidelity
  • Mixture of experts (Waiting GaussianMixtures package to work on v1.5)
  • Earth
  • Gradient Enhanced Kriging

ALL the currently available optimization methods:

  • SRBF
  • LCBS
  • DYCORS
  • EI
  • SOP
  • Multi-optimization: SMB and RTEA

Installing Surrogates package

using Pkg
Pkg.add("Surrogates")

Download Details:

Author: SciML
Source Code: https://github.com/SciML/Surrogates.jl 
License: View license

#julia #optimization 

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Surrogate Modeling and Optimization for Scientific Machine Learning
sophia tondon

sophia tondon

1620898103

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Hollie  Ratke

Hollie Ratke

1603753200

ML Optimization pt.1 - Gradient Descent with Python

So far in our journey through the Machine Learning universe, we covered several big topics. We investigated some regression algorithms, classification algorithms and algorithms that can be used for both types of problems (SVM**, **Decision Trees and Random Forest). Apart from that, we dipped our toes in unsupervised learning, saw how we can use this type of learning for clustering and learned about several clustering techniques.

We also talked about how to quantify machine learning model performance and how to improve it with regularization. In all these articles, we used Python for “from the scratch” implementations and libraries like TensorFlowPytorch and SciKit Learn. The word optimization popped out more than once in these articles, so in this and next article, we focus on optimization techniques which are an important part of the machine learning process.

In general, every machine learning algorithm is composed of three integral parts:

  1. loss function.
  2. Optimization criteria based on the loss function, like a cost function.
  3. Optimization technique – this process leverages training data to find a solution for optimization criteria (cost function).

As you were able to see in previous articles, some algorithms were created intuitively and didn’t have optimization criteria in mind. In fact, mathematical explanations of why and how these algorithms work were done later. Some of these algorithms are Decision Trees and kNN. Other algorithms, which were developed later had this thing in mind beforehand. SVMis one example.

During the training, we change the parameters of our machine learning model to try and minimize the loss function. However, the question of how do you change those parameters arises. Also, by how much should we change them during training and when. To answer all these questions we use optimizers. They put all different parts of the machine learning algorithm together. So far we mentioned Gradient Decent as an optimization technique, but we haven’t explored it in more detail. In this article, we focus on that and we cover the grandfather of all optimization techniques and its variation. Note that these techniques are not machine learning algorithms. They are solvers of minimization problems in which the function to minimize has a gradient in most points of its domain.

Dataset & Prerequisites

Data that we use in this article is the famous Boston Housing Dataset . This dataset is composed 14 features and contains information collected by the U.S Census Service concerning housing in the area of Boston Mass. It is a small dataset  with only 506 samples.

For the purpose of this article, make sure that you have installed the following _Python _libraries:

  • **NumPy **– Follow this guide if you need help with installation.
  • **SciKit Learn **– Follow this guide if you need help with installation.
  • Pandas – Follow this guide if you need help with installation.

Once installed make sure that you have imported all the necessary modules that are used in this tutorial.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import SGDRegressor

Apart from that, it would be good to be at least familiar with the basics of linear algebracalculus and probability.

Why do we use Optimizers?

Note that we also use simple Linear Regression in all examples. Due to the fact that we explore optimizationtechniques, we picked the easiest machine learning algorithm. You can see more details about Linear regression here. As a quick reminder the formula for linear regression goes like this:

where w and b are parameters of the machine learning algorithm. The entire point of the training process is to set the correct values to the w and b, so we get the desired output from the machine learning model. This means that we are trying to make the value of our error vector as small as possible, i.e. to find a global minimum of the cost function.

One way of solving this problem is to use calculus. We could compute derivatives and then use them to find places where is an extrema of the cost function. However, the cost function is not a function of one or a few variables; it is a function of all parameters of a machine learning algorithm, so these calculations will quickly grow into a monster. That is why we use these optimizers.

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Applications of machine learning in different industry domains

Machine learning applications are a staple of modern business in this digital age as they allow them to perform tasks on a scale and scope previously impossible to accomplish.Businesses from different domains realize the importance of incorporating machine learning in business processes.Today this trending technology transforming almost every single industry ,business from different industry domains hire dedicated machine learning developers for skyrocket the business growth.Following are the applications of machine learning in different industry domains.

Transportation industry

Machine learning is one of the technologies that have already begun their promising marks in the transportation industry.Autonomous Vehicles,Smartphone Apps,Traffic Management Solutions,Law Enforcement,Passenger Transportation etc are the applications of AI and ML in the transportation industry.Following challenges in the transportation industry can be solved by machine learning and Artificial Intelligence.

  • ML and AI can offer high security in the transportation industry.
  • It offers high reliability of their services or vehicles.
  • The adoption of this technology in the transportation industry can increase the efficiency of the service.
  • In the transportation industry ML helps scientists and engineers come up with far more environmentally sustainable methods for powering and operating vehicles and machinery for travel and transport.

Healthcare industry

Technology-enabled smart healthcare is the latest trend in the healthcare industry. Different areas of healthcare, such as patient care, medical records, billing, alternative models of staffing, IP capitalization, smart healthcare, and administrative and supply cost reduction. Hire dedicated machine learning developers for any of the following applications.

  • Identifying Diseases and Diagnosis
  • Drug Discovery and Manufacturing
  • Medical Imaging Diagnosis
  • Personalized Medicine
  • Machine Learning-based Behavioral Modification
  • Smart Health Records
  • Clinical Trial and Research
  • Better Radiotherapy
  • Crowdsourced Data Collection
  • Outbreak Prediction

**
Finance industry**

In financial industries organizations like banks, fintech, regulators and insurance are Adopting machine learning to improve their facilities.Following are the use cases of machine learning in finance.

  • Fraud prevention
  • Risk management
  • Investment predictions
  • Customer service
  • Digital assistants
  • Marketing
  • Network security
  • Loan underwriting
  • Algorithmic trading
  • Process automation
  • Document interpretation
  • Content creation
  • Trade settlements
  • Money-laundering prevention
  • Custom machine learning solutions

Education industry

Education industry is one of the industries which is investing in machine learning as it offers more efficient and easierlearning.AdaptiveLearning,IncreasingEfficiency,Learning Analytics,Predictive Analytics,Personalized Learning,Evaluating Assessments etc are the applications of machine learning in the education industry.

Outsource your machine learning solution to India,India is the best outsourcing destination offering best in class high performing tasks at an affordable price.Business** hire dedicated machine learning developers in India for making your machine learning app idea into reality.
**
Future of machine learning

Continuous technological advances are bound to hit the field of machine learning, which will shape the future of machine learning as an intensively evolving language.

  • Improved Unsupervised Algorithms
  • Increased Adoption of Quantum Computing
  • Enhanced Personalization
  • Improved Cognitive Services
  • Rise of Robots

**Conclusion
**
Today most of the business from different industries are hire machine learning developers in India and achieve their business goals. This technology may have multiple applications, and, interestingly, it hasn’t even started yet but having taken such a massive leap, it also opens up so many possibilities in the existing business models in such a short period of time. There is no question that the increase of machine learning also brings the demand for mobile apps, so most companies and agencies employ Android developers and hire iOS developers to incorporate machine learning features into them.

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Hire Machine Learning Developer | Hire ML Experts in India

Machine learning applications are a staple of modern business in this digital age as they allow them to perform tasks on a scale and scope previously impossible to accomplish.Businesses from different domains realize the importance of incorporating machine learning in business processes.Today this trending technology transforming almost every single industry ,business from different industry domains hire dedicated machine learning developers for skyrocket the business growth.Following are the applications of machine learning in different industry domains.

Transportation industry

Machine learning is one of the technologies that have already begun their promising marks in the transportation industry.Autonomous Vehicles,Smartphone Apps,Traffic Management Solutions,Law Enforcement,Passenger Transportation etc are the applications of AI and ML in the transportation industry.Following challenges in the transportation industry can be solved by machine learning and Artificial Intelligence.

  • ML and AI can offer high security in the transportation industry.
  • It offers high reliability of their services or vehicles.
  • The adoption of this technology in the transportation industry can increase the efficiency of the service.
  • In the transportation industry ML helps scientists and engineers come up with far more environmentally sustainable methods for powering and operating vehicles and machinery for travel and transport.

Healthcare industry

Technology-enabled smart healthcare is the latest trend in the healthcare industry. Different areas of healthcare, such as patient care, medical records, billing, alternative models of staffing, IP capitalization, smart healthcare, and administrative and supply cost reduction. Hire dedicated machine learning developers for any of the following applications.

  • Identifying Diseases and Diagnosis
  • Drug Discovery and Manufacturing
  • Medical Imaging Diagnosis
  • Personalized Medicine
  • Machine Learning-based Behavioral Modification
  • Smart Health Records
  • Clinical Trial and Research
  • Better Radiotherapy
  • Crowdsourced Data Collection
  • Outbreak Prediction

**
Finance industry**

In financial industries organizations like banks, fintech, regulators and insurance are Adopting machine learning to improve their facilities.Following are the use cases of machine learning in finance.

  • Fraud prevention
  • Risk management
  • Investment predictions
  • Customer service
  • Digital assistants
  • Marketing
  • Network security
  • Loan underwriting
  • Algorithmic trading
  • Process automation
  • Document interpretation
  • Content creation
  • Trade settlements
  • Money-laundering prevention
  • Custom machine learning solutions

Education industry

Education industry is one of the industries which is investing in machine learning as it offers more efficient and easierlearning.AdaptiveLearning,IncreasingEfficiency,Learning Analytics,Predictive Analytics,Personalized Learning,Evaluating Assessments etc are the applications of machine learning in the education industry.

Outsource your machine learning solution to India,India is the best outsourcing destination offering best in class high performing tasks at an affordable price.Business** hire dedicated machine learning developers in India for making your machine learning app idea into reality.
**
Future of machine learning

Continuous technological advances are bound to hit the field of machine learning, which will shape the future of machine learning as an intensively evolving language.

  • Improved Unsupervised Algorithms
  • Increased Adoption of Quantum Computing
  • Enhanced Personalization
  • Improved Cognitive Services
  • Rise of Robots

**Conclusion
**
Today most of the business from different industries are hire machine learning developers in India and achieve their business goals. This technology may have multiple applications, and, interestingly, it hasn’t even started yet but having taken such a massive leap, it also opens up so many possibilities in the existing business models in such a short period of time. There is no question that the increase of machine learning also brings the demand for mobile apps, so most companies and agencies employ Android developers and hire iOS developers to incorporate machine learning features into them.

#hire machine learning developers in india #hire dedicated machine learning developers in india #hire machine learning programmers in india #hire machine learning programmers #hire dedicated machine learning developers #hire machine learning developers