Faster, Leaner GPU Sklearn, Statsmodels written in PyTorch

Currently badges don't work --> will update later :)

50%+ Faster, 50%+ less RAM usage, GPU support re-written Sklearn, Statsmodels combo with new novel algorithms.

HyperLearn is written completely in PyTorch, NoGil Numba, Numpy, Pandas, Scipy & LAPACK, and mirrors (mostly) Scikit Learn. HyperLearn also has statistical inference measures embedded, and can be called just like Scikit Learn's syntax (model.confidence_interval_)

Time(s) is Fit + Predict. RAM(mb) = max( RAM(Fit), RAM(Predict) )

I've also added some preliminary results for N = 5000, P = 6000

Since timings are not good, I have submitted 2 bug reports to Scipy + PyTorch:

1. EIGH very very slow --> suggesting an easy fix #9212 scipy/scipy#9212
2. SVD very very slow and GELS gives nans, -inf #11174 pytorch/pytorch#11174

• Including Memory Sharing, Memory Management
• CUDA Parallelism through PyTorch & Numba

• Matrix Multiplication Ordering: https://en.wikipedia.org/wiki/Matrix_chain_multiplication
• Element Wise Matrix Multiplication reducing complexity to O(n^2) from O(n^3): https://en.wikipedia.org/wiki/Hadamard_product_(matrices)
• Reducing Matrix Operations to Einstein Notation: https://en.wikipedia.org/wiki/Einstein_notation
• Evaluating one-time Matrix Operations in succession to reduce RAM overhead.
• If p>>n, maybe decomposing X.T is better than X.
• Applying QR Decomposition then SVD might be faster in some cases.
• Utilise the structure of the matrix to compute faster inverse (eg triangular matrices, Hermitian matrices).
• Computing SVD(X) then getting pinv(X) is sometimes faster than pure pinv(X)

• Confidence, Prediction Intervals, Hypothesis Tests & Goodness of Fit tests for linear models are optimized.
• Using Einstein Notation & Hadamard Products where possible.
• Computing only what is necessary to compute (Diagonal of matrix and not entire matrix).
• Fixing the flaws of Statsmodels on notation, speed, memory issues and storage of variables.

• Using PyTorch to create Scikit-Learn like drop in replacements.

• Using Decorators & Functions where possible.
• Intuitive Middle Level Function names like (isTensor, isIterable).
• Handles Parallelism easily through hyperlearn.multiprocessing

• Matrix Completion algorithms - Non Negative Least Squares, NNMF
• Batch Similarity Latent Dirichelt Allocation (BS-LDA)
• Correlation Regression
• Feasible Generalized Least Squares FGLS
• Outlier Tolerant Regression
• Multidimensional Spline Regression
• Generalized MICE (any model drop in replacement)
• Using Uber's Pyro for Bayesian Deep Learning

* SVD/QR is the backbone for many algorithms including:
    * Linear & Ridge Regression (Regression)
    * Statistical Inference for Regression methods (Inference)
    * Principal Component Analysis (Dimensionality Reduction)
    * Linear & Quadratic Discriminant Analysis (Classification & Dimensionality Reduction)
    * Pseudoinverse, Truncated SVD (Linear Algebra)
    * Latent Semantic Indexing LSI (NLP)
    * (new methods) Correlation Regression, FGLS, Outlier Tolerant Regression, Generalized MICE, Splines (Regression)

1. Port all important Numpy functions to faster alternatives (ONGOING)

• Singular Value Decomposition (50% Complete) *