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This is a primer on machine learning for beginners. Certainly, there are plenty of excellent books on the subject, providing detailed explanations of many algorithms. The intent of this primer is not to outdo these texts in rigor; rather, to provide an introduction to the subject that is accessible, yet covers all the mathematical details, and provides implementations of most algorithms in Python. We feel this provides a well-rounded understanding of each algorithm: only by writing the code and seeing the math applied, and visually inspecting the algorithm's working, will a reader be fully able to connect all the dots. The style of the primer is largely conversational, and avoids too much formal jargon. We will certainly introduce all required technical terms, but while explaining an algorithm, we will use simple English and avoid unnecessarily formalisms. We hope this proves useful for individuals willing to seriously study the subject. [ABSTRACT FROM AUTHOR]

We present a novel theoretical framework for computing large, adaptive learning rates. Our framework makes minimal assumptions on the activations used and exploits the functional properties of the loss function. Specifically, we show that the inverse of the Lipschitz constant of the loss function is an ideal learning rate. We analytically compute formulas for the Lipschitz constant of several loss functions, and through extensive experimentation, demonstrate the strength of our approach using several architectures and datasets. In addition, we detail the computation of learning rates when other optimizers, namely, SGD with momentum, RMSprop, and Adam, are used. Compared to standard choices of learning rates, our approach converges faster, and yields better results. [ABSTRACT FROM AUTHOR]

Quantification of habitability is a complex task. Previous attempts at measuring habitability are well documented. Classification of exoplanets, on the other hand, is a different approach and depends on quality of training data available in habitable exoplanet catalogs. Classification is the task of predicting labels of newly discovered planets based on available class labels in the catalog. We present analytical exploration of novel activation functions as consequence of integration of several ideas leading to implementation and subsequent use in habitability classification of exoplanets. Neural networks, although a powerful engine in supervised methods, often require expensive tuning efforts for optimized performance. Habitability classes are hard to discriminate, especially when attributes used as hard markers of separation are removed from the data set. The solution is approached from the point of investigating analytical properties of the proposed activation functions. The theory of ordinary differential equations and fixed point are exploited to justify the "lack of tuning efforts" to achieve optimal performance compared to traditional activation functions. Additionally, the relationship between the proposed activation functions and the more popular ones is established through extensive analytical and empirical evidence. Finally, the activation functions have been implemented in plain vanilla feed-forward neural network to classify exoplanets. The mathematical exercise supplements the grand idea of classifying exoplanets, computing habitability scores/indices and automatic grouping of the exoplanets converging at some level. [ABSTRACT FROM AUTHOR]