AI News, Online Learning and Sub-Linear Debugging

Online Learning and Sub-Linear Debugging

They are often used for their computational desirability, e.g., for speed, the ability to consume large data sets, and the ability to handle non-convex objectives.

The prototypical supervised online learning algorithm receives an example, makes a prediction, receives a label and experiences a loss, and then makes an update to the model.If the examples are independent samples from the evaluation distribution, then the instantaneous loss experienced by the algorithm is an unbiased estimate of the generalization error.

By keeping track of this progressive validation loss, a practitioner can assess the impact of a proposed model change prior to consuming all the training input, hence sub-linear (in the training set size) debugging.

The new training data are prepared, but progressive validation loss on this new input is much worse than previous results after less than a minute of processing.

Roughly speaking, it is due the algorithm having to filter out all the poorly performing available models using finite training data, and therefore variance tends to increase whenever the model class is made more powerful without easing the search problem for the learning algorithm.

With these concepts in mind, let's consider some common scenarios: New features get introduced, and progressive validation loss is worse over the entire training run.

For similar reasons, with many learning algorithms adding new features cannot increase the bias, because the learning algorithm could choose not to use them (e.g., assign them zero weight in a linear model).

You might be tempted, under these conditions, to let the algorithm run for a long time in order to ultimately exceed previous performance, but this is a dangerous habit, as it defeats the purpose of sub-linear debugging.

Feeling satisfied, you let the algorithm run while you get some lunch, and, when you return, you discover that with more data the progressive loss improvement slowed and performance is now worse than under the old preprocessing.

The idea was right (“reduce variance by treating long words the same as their shorter prefixes”) but the strength had to be adjusted to fit the data resources (“with enough data, the best strategy is to treat words as different from their shorter prefixes”).

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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Machine Learning Algorithms: Which One to Choose for Your Problem

First of all, you should distinguish 4 types of Machine Learning tasks: Supervised learning is the task of inferring a function from labeled training data.

By fitting to the labeled training set, we want to find the most optimal model parameters to predict unknown labels on other objects (test set).

The method allows us to significantly improve accuracy, because we can use unlabeled data in the train set with a small amount of labeled data.

RL is an area of machine learning concerned with how software agents ought to take actions in some environment to maximize some notion of cumulative reward.

Now that we have some intuition about types of machine learning tasks, let’s explore the most popular algorithms with their applications in real life.

Your goal is to find the most optimal weights w1,…wn and bias for these features according to some loss function, for example, MSE or MAE for a regression problem.

In the case of MSE there is a mathematical equation from the least squares method: In practice, it’s easier to optimize it with gradient descent, that is much more computationally efficient.

Despite the simplicity of this algorithm, it works pretty well when you have thousands of features, for example, bag of words or n-gramms in text analysis.

More complex algorithms suffer from overfitting many features and not huge datasets, while linear regression provides decent quality.

Since this algorithm calculates the probability of belonging to each class, you should take into account how much the probability differs from 0 or 1 and average it over all objects as we did with linear regression.

If y equals 0, then the first addend under sum equals 0 and the second is the less the closer our predicted y_pred to 0 according to the properties of the logarithm.

It takes linear combination of features and applies non-linear function (sigmoid) to it, so it’s a very very small instance of neural network!

In regression trees we minimize the sum of a squared error between the predictive variable of the target values of the points that fall in that region and the one we assign to it.

Secondly, the result depends on the points randomly chosen at the beginning and the algorithm doesn’t guarantee that we’ll achieve the global minimum of the functional.

You have no chance to remember all the information, but you want to maximize information that you can remember in the time available, for example, learning first the theorems that occur in many exam tickets and so on.

hope that I could explain to you common perceptions of the most used machine learning algorithms and give intuition on how to choose one for your specific problem.

Loss Functions and Optimization Algorithms. Demystified.

The choice of Optimisation Algorithms and Loss Functions for a deep learning model can play a big role in producing optimum and faster results.

Consider a feature vector [x1, x2, x3] that is used to predict the probability (p) of occurrence of a certain event.

Weighing factors: Each input in the feature vector is assigned its own relative weight (w), which decides the impact that the particular input needs in the summation function.

In relatively easier terms, some inputs are made more important than others by giving them more weight so that they have a greater effect in the summation function (y).

Activation function: The result of the summation function, that is the weighted sum, is transformed to a desired output by employing a non linear function (fNL), also known as activation function.

Since the desired output is probability of an event in this case, a sigmoid function can be used to restrict the results (y) between 0 and 1.

One of the most widely used loss function is mean square error, which calculates the square of difference between actual value and predicted value.

The current error is typically propagated backwards to a previous layer, where it is used to modify the weights and bias in such a way that the error is minimized.

the partial derivative of loss function with respect to weights, and the weights are modified in the opposite direction of the calculated gradient.

Thus, the components of a neural network model i.e the activation function, loss function and optimization algorithm play a very important role in efficiently and effectively training a Model and produce accurate results.

Loss functions fall under four major category: Regressive loss functions:They are used in case of regressive problems, that is when the target variable is continuous.

Classification loss functions: The output variable in classification problem is usually a probability value f(x), called the score for the input x.

The target variable y, is a binary variable, 1 for true and -1 for false. On an example (x,y), the margin is defined as yf(x).

Thus it was more sensitive to outliers and pushed pixel value towards 1 (in our case, white as can be seen in image after first epoch itself).

A learning rate that is too small leads to painfully slow convergence i.e will result in small baby steps towards finding optimal parameter values which minimize loss and finding that valley which directly affects the overall training time which gets too large.

Adaptive Learning Algorithms: The challenge of using gradient descent is that their hyper parameters have to be defined in advance and they depend heavily on the type of model and problem.

They have per-paramter learning rate methods, which provide heuristic approach without requiring expensive work in tuning hyperparameters for the learning rate schedule manually.

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