AI News, First machine learning method capable of accurate extrapolation

First machine learning method capable of accurate extrapolation

In the past, machine learning was only capable of interpolating data -- making predictions about situations that are 'between' other, known situations.

It was incapable of extrapolating -- making predictions about situations outside of the known -- because it learns to fit the known data as closely as possible locally, regardless of how it performs outside of these situations.

Sahoo, a PhD student also at MPI for Intelligent Systems, and Christoph Lampert, professor at IST Austria, developed a new machine learning method that addresses these problems, and is the first machine learning method to accurately extrapolate to unseen situations.

In the future, the robot would experiment with different motions, then be able to use machine learning to uncover the equations that govern its body and movement, allowing it to avoid dangerous actions or situations,' adds Martius.

While robots are one active area of research, the method can be used with any type of data, from biological systems to X-ray transition energies, and can also be incorporated into larger machine learning networks.

First machine learning method capable of accurate extrapolation

In the past, machine learning was only capable of interpolating data—making predictions about situations that are 'between' other, known situations.

It was incapable of extrapolating—making predictions about situations outside of the known—because it learns to fit the known data as closely as possible locally, regardless of how it performs outside of these situations.

In addition, collecting sufficient data for effective interpolation is both time- and resource-intensive, and requires data from extreme or dangerous situations.

student also at MPI for Intelligent Systems, and Christoph Lampert, professor at IST Austria, developed a new machine learning method that addresses these problems, and is the first machine learning method to accurately extrapolate to unseen situations.

The key feature of the new method is that it strives to reveal the true dynamics of the situation: it takes in data and returns the equations that describe the underlying physics.

In the new method, the resulting equations are far simpler: 'Our method's equations are something you would see in a textbook—simple and intuitive,' says Christoph Lampert.

The latter is another key difference: other machine learning methods give no insight into the relationship between conditions and results—and thus, no intuition on whether the model is even plausible.

Finally, in order to guarantee interpretability and optimize for physical situations, the team based their learning method on a different type of framework.

This new design is simpler than previous methods, which in practice means that less data is needed to give the same or even better results.

Machine Learning

Supervised machine learning builds a model that makes predictions based on evidence in the presence of uncertainty.

A supervised learning algorithm takes a known set of input data and known responses to the data (output) and trains a model to generate reasonable predictions for the response to new data.

Common algorithms for performing classification include support vector machine (SVM), boosted and bagged decision trees, k-nearest neighbor, Naïve Bayes, discriminant analysis, logistic regression, and neural networks.

Common regression algorithms include linear model, nonlinear model, regularization, stepwise regression, boosted and bagged decision trees, neural networks, and adaptive neuro-fuzzy learning.

Supervised learning

Supervised learning is the machine learning task of learning a function that maps an input to an output based on example input-output pairs.[1]

In supervised learning, each example is a pair consisting of an input object (typically a vector) and a desired output value (also called the supervisory signal).

A supervised learning algorithm analyzes the training data and produces an inferred function, which can be used for mapping new examples.

An optimal scenario will allow for the algorithm to correctly determine the class labels for unseen instances.

This requires the learning algorithm to generalize from the training data to unseen situations in a 'reasonable' way (see inductive bias).

There is no single learning algorithm that works best on all supervised learning problems (see the No free lunch theorem).

The prediction error of a learned classifier is related to the sum of the bias and the variance of the learning algorithm.[4]

But if the learning algorithm is too flexible, it will fit each training data set differently, and hence have high variance.

A key aspect of many supervised learning methods is that they are able to adjust this tradeoff between bias and variance (either automatically or by providing a bias/variance parameter that the user can adjust).

The second issue is the amount of training data available relative to the complexity of the 'true' function (classifier or regression function).

If the true function is simple, then an 'inflexible' learning algorithm with high bias and low variance will be able to learn it from a small amount of data.

But if the true function is highly complex (e.g., because it involves complex interactions among many different input features and behaves differently in different parts of the input space), then the function will only be learnable from a very large amount of training data and using a 'flexible' learning algorithm with low bias and high variance.

If the input feature vectors have very high dimension, the learning problem can be difficult even if the true function only depends on a small number of those features.

Hence, high input dimensionality typically requires tuning the classifier to have low variance and high bias.

In practice, if the engineer can manually remove irrelevant features from the input data, this is likely to improve the accuracy of the learned function.

In addition, there are many algorithms for feature selection that seek to identify the relevant features and discard the irrelevant ones.

This is an instance of the more general strategy of dimensionality reduction, which seeks to map the input data into a lower-dimensional space prior to running the supervised learning algorithm.

fourth issue is the degree of noise in the desired output values (the supervisory target variables).

If the desired output values are often incorrect (because of human error or sensor errors), then the learning algorithm should not attempt to find a function that exactly matches the training examples.

You can overfit even when there are no measurement errors (stochastic noise) if the function you are trying to learn is too complex for your learning model.

In such a situation, the part of the target function that cannot be modeled 'corrupts' your training data - this phenomenon has been called deterministic noise.

In practice, there are several approaches to alleviate noise in the output values such as early stopping to prevent overfitting as well as detecting and removing the noisy training examples prior to training the supervised learning algorithm.

There are several algorithms that identify noisy training examples and removing the suspected noisy training examples prior to training has decreased generalization error with statistical significance.[5][6]

When considering a new application, the engineer can compare multiple learning algorithms and experimentally determine which one works best on the problem at hand (see cross validation).

Given fixed resources, it is often better to spend more time collecting additional training data and more informative features than it is to spend extra time tuning the learning algorithms.

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For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

In both cases, it is assumed that the training set consists of a sample of independent and identically distributed pairs,

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In order to measure how well a function fits the training data, a loss function

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Hence, a supervised learning algorithm can be constructed by applying an optimization algorithm to find

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contains many candidate functions or the training set is not sufficiently large, empirical risk minimization leads to high variance and poor generalization.

The regularization penalty can be viewed as implementing a form of Occam's razor that prefers simpler functions over more complex ones.

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The training methods described above are discriminative training methods, because they seek to find a function

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Introductory guide on Linear Programming for (aspiring) data scientists

From using your time productively to solving supply chain problems for your company –

So, I thought let me do justice to this awesome technique. I decided to write an article which explains Linear programming in simple English.

Linear programming is a simple technique where we depict complex relationships through linear functions and then find the optimum points.

You are using linear programming when you are driving from home to work and want to take the shortest route.

So, the delivery person will calculate different routes for going to all the 6 destinations and then come up with the shortest route.

In this case, the objective of the delivery person is to deliver the parcel on time at all 6 destinations.

But with a simple assumption, we have reduced the complexity of the problem drastically and are creating a solution which should work in most scenarios.

 To manufacture each unit of A and B, following quantities are required: The company kitchen has a total of 5 units of Milk and 12 units of Choco.

Let the total number of units produced of A be = X Let the total number of units produced of B be = Y Now, the total profit is represented by Z The total profit the company makes is given by the total number of units of A and B produced multiplied by its per unit profit Rs 6 and Rs 5 respectively.

Let us look at the steps of defining a Linear Programming problem generically: For a problem to be a linear programming problem, the decision variables, objective function and constraints all have to be linear functions.

graphical method involves formulating a set of linear inequalities subject to the constraints.

He wants to know how to plant each variety in the 110 hectares, given the costs, net profits and labor requirements according to the data shown below: The farmer has a budget of US$10,000 and an availability of 1,200 man-days during the planning horizon.

Step 1: Identify the decision variables The total area for growing Wheat = X (in hectares) The total area for growing Barley  = Y (in hectares) X

The next constraint is, the upper cap on the availability on the total number of man-days for planning horizon.

Plot the first 2 lines on a graph in first quadrant (like shown below) The optimal feasible solution is achieved at the point of intersection where the budget &

This means the point at which the equations X + 2Y ≤ 100 and X + 3Y ≤ 120 intersect gives us the optimal solution.

To maximize profit the farmer should produce Wheat and Barley in 60 hectares and 20 hectares of land respectively.

The maximum profit the company will gain is, Max Z = 50 * (60) + 120 * (20) =

In reality, a linear program can contain 30 to 1000 variables and solving it either Graphically or Algebraically is next to impossible.

Example: Below there is a diet chart which gives me calories, protien, carbohydrate and fat content for 4 food items.

The diet chart is as follows: The chart gives the nutrient content as well as the per-unit cost of each food item.

The diet has to be planned in such a way that it should contain at least 500 calories, 6 grams of protien, 10 grams of carbohydrates and 8 grams of fat.

The total cost is given by the sumproduct of number of units eaten and per unit cost.

popular methods for linear programming. Simplex method is an iterative procedure for getting the most feasible solution.

In this method, we keep transforming the value of basic variables to get maximum value for the objective function.

linear programming function is in its standard form if it seeks to maximize the objective function. subject to constraints, .

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The local newspaper limits the number of advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than half of the total number of advertisements should occur on the radio.

Step 1: Identify Decision Variables Let , ,    represent the total number of ads for television, newspaper, and radio respectively.

And the individual costs per television, newspaper and radio advertisement is $2000, $600 and $300 respectively.

Northwest corner method is a special type method used for transportation problems in linear programming.

The model is based on the hypothesis that the total demand is equal to the total supply, i.e the model is balanced.

(A silo is a storage area of farm used to store grain and Mill is a grinding factory for grains).

The cost of transportation from Silo i to Mill j is given by the cost in each cell corresponding to the supply from  each silo 1 and the demand at each Mill.

For example: The cost of transporting from Silo 1 to Mill 1 is $10, from Silo 3 to Mill 5 is $18.

As the name suggests Northwest corner method is a method of allocating the units starting from the topleft cell.

The demand for Mill 2 is 15 units, which it can get 10 units from Silo 1 at a cost of $2 per unit and 5  units from Silo 2 at a cost of $7 per unit.

The demand for Mill 3 is 15 units, which it can get from Silo 2 at a cost of $9 per unit.

It will get 5 units from a Silo 2 at a cost of $20 per unit and 10 units from Silo 3 at a cost of $18 per unit.

So, for the above problem, I supply 5 units from Silo 3 at per unit cost of $4.

Then for Mill 4 we supply 10 units from Silo 2 at per unit cost of $20 and 5 units from Silo 3 a $18 per unit.

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