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

A new method developed by scientists at the Institute of Science and Technology Austria (IST Austria) and the Max Planck Institute for Intelligent Systems (MPI for Intelligent Systems) is the first machine learning method that can use observations made under safe conditions to make accurate predictions for all possible conditions governed by the same physical dynamics.

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.

“If you know those equations,” says Georg Martius, “then you can say what will happen in all situations, even if you haven’t seen them.” In other words, this is what allows the method to extrapolate reliably, making it unique among machine learning methods.

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.

PMLR, 2018.http://proceedings.mlr.press/v80/sahoo18a.htmlArxiv Preprint: arxiv.org/abs/1806.07259 Link to conference: icml.cc This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 291734.The research received funding from the ISTFELLOW program, a Marie Skłodowska-Curie COFUND grant co-funded by IST Austria and the European Union through the Horizon 2020 research and innovation programme.

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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Bayesian Statistics explained to Beginners in Simple English

Bayesian Statistics continues to remain incomprehensible in the ignited minds of many analysts.

Before we actually delve in Bayesian Statistics, let us spend a few minutes understanding Frequentist Statistics, the more popular version of statistics most of us come across and the inherent problems in that.

It calculates the probability of an event in the long run of the experiment (i.e the experiment is repeated under the same conditions to obtain the outcome).

For example, I perform an experiment with a stopping intention in mind that I will stop the experiment when it is repeated 1000 times or I see minimum 300 heads in a coin toss.

An important thing is to note that, though the difference between the actual number of heads and expected number of heads( 50% of number of tosses) increases as the number of tosses are increased, the proportion of number of heads to total number of tosses approaches 0.5 (for a fair coin).

This experiment presents us with a very common flaw found in frequentist approach i.e. Dependence of the result of an experiment on the number of times the experiment is repeated.

20th century saw a massive upsurge in the frequentist statistics being applied to numerical models to check whether one sample is different from the other, a parameter is important enough to be kept in the model and variousother  manifestations of hypothesis testing.

But frequentist statistics suffered some great flaws in its design and interpretation  which posed a serious concern in all real life problems.

p-values measured against a sample (fixed size) statistic with some stopping intention changes with change in intention and sample size.

For example: Person A may choose to stop tossing a coin when the total count reaches 100 while B stops at 1000.

This makes the stopping potential absolutely absurd since no matter how many persons perform the tests on the same data, the results should be consistent.

Therefore, Substituting the values in the conditional probability formula, we get the probability to be around 50%, which is almost the double of 25% when rain was not taken into account (Solve it at your end).

This further strengthened our belief  of  James winning in the light of new evidence i.e rain. You must be wondering that this formula bears close resemblance to something you might have heard a lot about.

We should be more interested in knowing : Given an outcome (D) what is the probbaility of coin being fair (θ=0.5) Lets represent it using Bayes Theorem: P(θ|D)=(P(D|θ) X P(θ))/P(D) Here, P(θ) is the prior i.e the strength of our belief in the fairness of coin before the toss.

If we knew that coin was fair, this gives the probability of observing the number of heads in a particular number of flips.

This is the probability of data as determined by summing (or integrating) across all possible values of θ, weighted by how strongly we believe in those particular values of θ.

If we had multiple views of what the fairness of the coin is (but didn’t know for sure), then this tells us the probability of seeing a certain sequence of flips for all possibilities of our belief in the coin’s fairness.

One to represent the likelihood function P(D|θ)  and the other for representing the distribution of prior beliefs . The product of these two gives the posterior belief P(θ|D) distribution.

It is the probability of observing a particular number of heads in a particular number of flips for a given fairness of coin.

It is worth noticing that representing 1 as heads and 0 as tails is just a mathematical notation to formulate a model. We can combine the above mathematical definitions into a single definition to represent the probability of both the outcomes.

Well, the mathematical function used to represent the prior beliefs is known as beta distribution. It has some very nice mathematical properties which enable us to model our beliefs about a binomial distribution.

Note: α and β are intuitive to understand since they can be calculated by knowing the mean (μ) and standard deviation (σ) of the distribution.

This is because when we multiply it with a likelihood function, posterior distribution yields a form similar to the prior distribution which is much easier to relate to and understand.

This is interesting. Just knowing the mean and standard distribution of our belief about the parameter θ and by observing the number of heads in N flips, we can update our belief about the model parameter(θ).

Let’s see how our prior and posterior beliefs are going to look: prior = P(θ|α,β)=P(θ|13.8,9.2) Posterior = P(θ|z+α,N-z+β)=P(θ|93.8,29.2) Lets visualize both the beliefs on a graph:

Without going into the rigorous mathematical structures, this section will provide you a quick overview of different approaches of frequentist and bayesian methods to test for significance and difference between groups and which method is most reliable.

We can interpret p values as (taking an example of p-value as 0.02 for a distribution of mean 100) : There is 2% probability that the sample will have mean equal to 100.

A p-value less than 5% does not guarantee that null hypothesis is wrong nor a p-value greater than 5% ensures that null hypothesis is right.

The null hypothesis in bayesian framework assumes ∞ probability distribution only at a particular value of a parameter (say θ=0.5) and a zero probability else where.

Part III will be based on creating a Bayesian regression model from scratch and interpreting its results in R. So, before I start with Part II, I would like to have your suggestions / feedback on this article.

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