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Machine learning, in numpy

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Ever wish you had an inefficient but somewhat legible collection of machine learning algorithms implemented exclusively in NumPy? No?


For rapid experimentation

To use this code as a starting point for ML prototyping / experimentation, just clone the repository, create a new virtualenv, and start hacking:

$ git clone
$ cd numpy-ml && virtualenv npml && source npml/bin/activate
$ pip3 install -r requirements-dev.txt

As a package

If you don't plan to modify the source, you can also install numpy-ml as a Python package:

pip3 install -u numpy_ml

The reinforcement learning agents train on environments defined in the OpenAI gym. To install these alongside numpy-ml, you can use

pip3 install -u 'numpy_ml[rl]'


For more details on the available models, see the project documentation.

Available models

  1. Gaussian mixture model

    • EM training
  2. Hidden Markov model

    • Viterbi decoding
    • Likelihood computation
    • MLE parameter estimation via Baum-Welch/forward-backward algorithm
  3. Latent Dirichlet allocation (topic model)

    • Standard model with MLE parameter estimation via variational EM
    • Smoothed model with MAP parameter estimation via MCMC
  4. Neural networks

    • Layers / Layer-wise ops
      • Add
      • Flatten
      • Multiply
      • Softmax
      • Fully-connected/Dense
      • Sparse evolutionary connections
      • LSTM
      • Elman-style RNN
      • Max + average pooling
      • Dot-product attention
      • Embedding layer
      • Restricted Boltzmann machine (w. CD-n training)
      • 2D deconvolution (w. padding and stride)
      • 2D convolution (w. padding, dilation, and stride)
      • 1D convolution (w. padding, dilation, stride, and causality)
    • Modules
      • Bidirectional LSTM
      • ResNet-style residual blocks (identity and convolution)
      • WaveNet-style residual blocks with dilated causal convolutions
      • Transformer-style multi-headed scaled dot product attention
    • Regularizers
      • Dropout
    • Normalization
      • Batch normalization (spatial and temporal)
      • Layer normalization (spatial and temporal)
    • Optimizers
      • SGD w/ momentum
      • AdaGrad
      • RMSProp
      • Adam
    • Learning Rate Schedulers
      • Constant
      • Exponential
      • Noam/Transformer
      • Dlib scheduler
    • Weight Initializers
      • Glorot/Xavier uniform and normal
      • He/Kaiming uniform and normal
      • Standard and truncated normal
    • Losses
      • Cross entropy
      • Squared error
      • Bernoulli VAE loss
      • Wasserstein loss with gradient penalty
      • Noise contrastive estimation loss
    • Activations
      • ReLU
      • Tanh
      • Affine
      • Sigmoid
      • Leaky ReLU
      • ELU
      • SELU
      • Exponential
      • Hard Sigmoid
      • Softplus
    • Models
      • Bernoulli variational autoencoder
      • Wasserstein GAN with gradient penalty
      • word2vec encoder with skip-gram and CBOW architectures
    • Utilities
      • col2im
        (MATLAB port)
      • im2col
        (MATLAB port)
      • conv1D
      • conv2D
      • deconv2D
      • minibatch
  5. Tree-based models

    • Decision trees (CART)
    • [Bagging] Random forests
    • [Boosting] Gradient-boosted decision trees
  6. Linear models

    • Ridge regression
    • Logistic regression
    • Ordinary least squares
    • Bayesian linear regression w/ conjugate priors
      • Unknown mean, known variance (Gaussian prior)
      • Unknown mean, unknown variance (Normal-Gamma / Normal-Inverse-Wishart prior)
  7. n-Gram sequence models

    • Maximum likelihood scores
    • Additive/Lidstone smoothing
    • Simple Good-Turing smoothing
  8. Multi-armed bandit models

    • UCB1
    • LinUCB
    • Epsilon-greedy
    • Thompson sampling w/ conjugate priors
      • Beta-Bernoulli sampler
    • LinUCB
  9. Reinforcement learning models

    • Cross-entropy method agent
    • First visit on-policy Monte Carlo agent
    • Weighted incremental importance sampling Monte Carlo agent
    • Expected SARSA agent
    • TD-0 Q-learning agent
    • Dyna-Q / Dyna-Q+ with prioritized sweeping
  10. Nonparameteric models

    • Nadaraya-Watson kernel regression
    • k-Nearest neighbors classification and regression
    • Gaussian process regression
  11. Matrix factorization

    • Regularized alternating least-squares
    • Non-negative matrix factorization
  12. Preprocessing

    • Discrete Fourier transform (1D signals)
    • Discrete cosine transform (type-II) (1D signals)
    • Bilinear interpolation (2D signals)
    • Nearest neighbor interpolation (1D and 2D signals)
    • Autocorrelation (1D signals)
    • Signal windowing
    • Text tokenization
    • Feature hashing
    • Feature standardization
    • One-hot encoding / decoding
    • Huffman coding / decoding
    • Term frequency-inverse document frequency (TF-IDF) encoding
    • MFCC encoding
  13. Utilities

    • Similarity kernels
    • Distance metrics
    • Priority queue
    • Ball tree
    • Discrete sampler
    • Graph processing and generators


Am I missing your favorite model? Is there something that could be cleaner / less confusing? Did I mess something up? Submit a PR! The only requirement is that your models are written with just the Python standard library and NumPy. The SciPy library is also permitted under special circumstances ;)

See full contributing guidelines here.

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