WAX-ML: A Python library for machine-learning and feedback loops on streaming data

Quickstart | Install guide | Change logs | Reference docs

Introduction

🌊 Wax is what you put on a surfboard to avoid slipping. It is an essential tool to go surfing ... 🌊

WAX-ML is a research-oriented Python library providing tools to design powerful machine learning algorithms and feedback loops working on streaming data.

It strives to complement JAX with tools dedicated to time series.

WAX-ML makes JAX-based programs easy to use for end-users working with pandas and xarray for data manipulation.

WAX-ML provides a simple mechanism for implementing feedback loops, allows the implementation of reinforcement learning algorithms with functions, and makes them easy to integrate by end-users working with the object-oriented reinforcement learning framework from the Gym library.

To learn more, you can read our article on ArXiv or simply access the code in this repository.

WAX-ML Goal

WAX-ML's goal is to expose "traditional" algorithms that are often difficult to find in standard Python ecosystem and are related to time-series and more generally to streaming data.

It aims to make it easy to work with algorithms from very various computational domains such as machine learning, online learning, reinforcement learning, optimal control, time-series analysis, optimization, statistical modeling.

For now, WAX-ML focuses on time-series algorithms as this is one of the areas of machine learning that lacks the most dedicated tools. Working with time series is notoriously known to be difficult and often requires very specific algorithms (statistical modeling, filtering, optimal control).

Even though some of the modern machine learning methods such as RNN, LSTM, or reinforcement learning can do an excellent job on some specific time-series problems, most of the problems require using more traditional algorithms such as linear and non-linear filters, FFT, the eigendecomposition of matrices (e.g. [7]), principal component analysis (PCA) (e.g. [8]), Riccati solvers for optimal control and filtering, ...

By adopting a functional approach, inherited from JAX, WAX-ML aims to be an efficient tool to combine modern machine learning approaches with more traditional ones.

Some work has been done in this direction in [2] in References where transformer encoder architectures are massively accelerated, with limited accuracy costs, by replacing the self-attention sublayers with a standard, non-parameterized Fast Fourier Transform (FFT).

WAX-ML may also be useful for developing research ideas in areas such as online machine learning (see [1] in References) and development of control, reinforcement learning, and online optimization methods.

What does WAX-ML do?

Well, building WAX-ML, we have some pretty ambitious design and implementation goals.

To do things right, we decided to start small and in an open-source design from the beginning.

For now, WAX-ML contains:

• transformation tools that we call "unroll" transformations allowing us to apply any transformation, possibly stateful, on sequential data. It generalizes the RNN architecture to any stateful transformation allowing the implementation of any kind of "filter".

• a "stream" module, described in 🌊 Streaming Data 🌊, permitting us to synchronize data streams with different time resolutions.

• some general pandas and xarray "accessors" permitting the application of any JAX-functions on pandas and xarray data containers: DataFrame, Series, Dataset, and DataArray.

• ready-to-use exponential moving average filter that we exposed with two APIs:

  • one for JAX users: as Haiku modules (EWMA, ... see the complete list in our API documentation ).
  • a second one for pandas and xarray users: with drop-in replacement of pandas ewm accessor.

• a simple module OnlineSupervisedLearner to implement online learning algorithms for supervised machine learning problems.

• building blocks for designing feedback loops in reinforcement learning, and have provided a module called GymFeedback allowing the implementation of feedback loop as the introduced in the library Gym, and illustrated this figure:

  

What is JAX?

JAX is a research-oriented computational system implemented in Python that leverages the XLA optimization framework for machine learning computations. It makes XLA usable with the NumPy API and some functional primitives for just-in-time compilation, differentiation, vectorization, and parallelization. It allows building higher-level transformations or "programs" in a functional programming approach. See JAX's page for more details.

Why to use WAX-ML?

If you deal with time-series and are a pandas or xarray user, b ut you want to use the impressive tools of the JAX ecosystem, then WAX-ML might be the right tool for you, as it implements pandas and xarray accessors to apply JAX functions.

If you are a user of JAX, you may be interested in adding WAX-ML to your toolbox to address time-series problems.

Design

Research oriented

WAX-ML is a research-oriented library. It relies on JAX and Haiku functional programming paradigm to ease the development of research ideas.

WAX-ML is a bit like Flux in Julia programming language.

Functional programming

In WAX-ML, we pursue a functional programming approach inherited from JAX.

In this sense, WAX-ML is not a framework, as most object-oriented libraries offer. Instead, we implement "functions" that must be pure to exploit the JAX ecosystem.

Haiku modules

We use the "module" mechanism proposed by the Haiku library to easily generate pure function pairs, called init and apply in Haiku, to implement programs that require the management of parameters and/or state variables. You can see the Haiku module API and Haiku transformation functions for more details.

In this way, we can recover all the advantages of object-oriented programming but exposed in the functional programming approach. It permits to ease the development of robust and reusable features and to develop "mini-languages" tailored to specific scientific domains.

WAX-ML works with other libraries

We want existing machine learning libraries to work well together while trying to leverage their strength. This is facilitated with a functional programming approach.

WAX-ML is not a framework but either a set of tools that aim to complement JAX Ecosystem.

Contents

• 🚀 Quickstart: Colab in the Cloud 🚀
• ⏱ Synchronize streams ⏱
• 🌊 Streaming Data 🌊
• Implemented modules
• ♻ Feedback loops ♻
• Future plans
• ⚒ Installation ⚒
• Disclaimer
• Development
• References
• License
• Citing WAX-ML
• Reference documentation

🚀 Quickstart 🚀

Jump right in using a notebook in your browser, connected to a Google Cloud GPU or simply read our notebook in the documentation.

Here are some starter notebooks:

• 〰 Compute exponential moving averages with xarray and pandas accessors 〰 : , Open in Documentation
• ⏱ Synchronize data streams ⏱ : , Open in Documentation
• 🌡 Binning temperatures 🌡 : , Open in Documentation
• 🎛 The three steps workflow 🎛 : , Open in Documentation
• 🔭 Reconstructing the light curve of stars with LSTM 🔭: , Open in Documentation
• 🦎 Online linear regression with a non-stationary environment 🦎: , Open in Documentation

⏱ Synchronize streams ⏱

Physicists have brought a solution to the synchronization problem called the Poincaré–Einstein synchronization (See Poincaré-Einstein synchronization Wikipedia page). In WAX-ML we have implemented a similar mechanism by defining a "local time", borrowing Henri Poincaré terminology, to denominate the timestamps of the stream (the "local stream") in which the user wants to apply transformations and unravel all other streams. The other streams, which we have called "secondary streams", are pushed back in the local stream using embedding maps which specify how to convert timestamps from a secondary stream into timestamps in the local stream.

This synchronization mechanism permits to work with secondary streams having timestamps at frequencies that can be lower or higher than the local stream. The data from these secondary streams are represented in the "local stream" either with the use of a forward filling mechanism for lower frequencies or with a buffering mechanism for higher frequencies.

Note that this simple synchronization scheme assumes that the different event streams have fixed latencies.

We have implemented a "data tracing" mechanism to optimize access to out-of-sync streams. This mechanism works on in-memory data. We perform the first pass on the data, without actually accessing it, and determine the indices necessary to later access the data. Doing so we are vigilant to not let any "future" information pass through and thus guaranty a data processing that respects causality.

The buffering mechanism used in the case of higher frequencies works with a fixed buffer size (see the WAX-ML module wax.modules.Buffer to allow the use of JAX / XLA optimizations and efficient processing.

Example

Let's illustrate with a small example how wax.stream.Stream synchronizes data streams.

Let's use the dataset "air temperature" with :

• An air temperature is defined with hourly resolution.
• A "fake" ground temperature is defined with a daily resolution as the air temperature minus 10 degrees.

from wax.accessors import register_wax_accessors

register_wax_accessors()

from wax.modules import EWMA


def my_custom_function(dataset):
    return {
        "air_10": EWMA(1.0 / 10.0)(dataset["air"]),
        "air_100": EWMA(1.0 / 100.0)(dataset["air"]),
        "ground_100": EWMA(1.0 / 100.0)(dataset["ground"]),
    }

results, state = dataset.wax.stream(
    local_time="time", ffills={"day": 1}, pbar=True
).apply(my_custom_function, format_dims=dataset.air.dims)

_ = results.isel(lat=0, lon=0).drop(["lat", "lon"]).to_pandas().plot(figsize=(12, 8))

🌊 Streaming Data 🌊

WAX-ML may complement JAX ecosystem by adding support for streaming data.

To do this, WAX-ML implements a unique data tracing mechanism that prepares for fast access to in-memory data and allows the execution of JAX tractable functions such as jit, grad, vmap, or pmap.

This mechanism is somewhat special in that it works with time-series data.

The wax.stream.Stream object implements this idea. It uses Python generators to synchronize multiple streaming data streams with potentially different temporal resolutions.

The wax.stream.Stream object works on in-memory data stored in xarray.Dataset.

To work with "real" streaming data, it should be possible to implement a buffer mechanism running on any Python generator and to use the synchronization and data tracing mechanisms implemented in WAX-ML to apply JAX transformations on batches of data stored in memory. (See our WEP4 enhancement proposal)

⌛ Adding support for time dtypes in JAX ⌛

At the moment datetime64 and string_ dtypes are not supported in JAX.

WAX-ML add support for datetime64 and string_ NumPy dtypes in JAX. To do so, WAX-ML implements:

• an encoding scheme for datetime64 relying on pairs of 32-bit integers similar to PRNGKey in JAX.
• an encoding scheme for string_ relying on LabelEncoder of Scikit-learn.

By providing these two encoding schemes, WAX-ML makes it easy to use JAX algorithms on data of these types.

Currently, the types of time offsets supported by WAX-ML are quite limited and we collaborate with the pandas, xarray, and Astropy teams to further develop the time manipulation tools in WAX-ML (see "WEP1" in WEP.md).

pandas and xarray accessors

WAX-ML implements pandas and xarray accessors to ease the usage of machine-learning algorithms implemented with functions implemented with Haiku modules on high-level data APIs :

• pandas's DataFrame and Series
• xarray's Dataset and DataArray.

To load the accessors, run:

from wax.accessors import register_wax_accessors
register_wax_accessors()

Then run the "one-liner" syntax:

<data-container>.stream(…).apply(…)

Implemented modules

We have some modules (inherited from Haiku modules) ready to be used in wax.modules (see our api documentation).

They can be considered as "building blocks" that can be reused to build more advanced programs to run on streaming data.

Fundamental modules

We have some "fundamental" modules that are specific to time series management,

• the Buffer module which implements the buffering mechanism
• the UpdateOnEvent module which allows to "freeze" the computation of a program and to update it on some events in the "local flow". To illustrate the use of this module we show how it can be used to compute the opening, high and closing quantities of temperatures recorded during a day, the binning process being reset at each day change. We show an illustrative graph of the final result:

pandas modules

We have a few more specific modules that aim to reproduce some of the logic that pandas users may be familiar with, such as:

• Lag to implement a delay on the input data
• Diff to compute differences between values over time
• PctChange to compute the relative difference between values over time.
• RollingMean to compute the moving average over time.
• EWMA, EWMVar, EWMCov, to compute the exponential moving average, variance, covariance of the input data.

Online learning and reinforcement learning modules

Finally, we implement domain-specific modules for online learning and reinforcement learning such as OnlineSupervisedLearner and GymFeedback (see dedicated sections).

accessors

For now, WAX-ML offers direct access to some modules through specific accessors for pandas and xarray users. For instance, we have an implementation of the "exponential moving average" directly accessible through the accessor <data-container>.ewm(...).mean() which provides a drop-in replacement for the exponential moving average of pandas.

For now, WAX-ML offers direct access to some modules through specific accessors for pandas and xarray users.

For instance, you can see our implementation of the "exponential moving average". This is a drop-in replacement for the exponential moving average of pandas.

Let's show how it works on the "air temperature" dataset from xarray.tutorials:

import xarray as xr
da = xr.tutorial.open_dataset("air_temperature")
dataframe = da.air.to_series().unstack(["lon", "lat"])

Pandas ewma:

air_temp_ewma = dataframe.ewm(alpha=1.0 / 10.0).mean()

WAX-ML ewma:

air_temp_ewma = dataframe.wax.ewm(alpha=1.0 / 10.0).mean()

Apply a custom function to a Dataset

Now let's illustrate how WAX-ML accessors work on xarray datasets.

from wax.modules import EWMA


def my_custom_function(dataset):
    return {
        "air_10": EWMA(1.0 / 10.0)(dataset["air"]),
        "air_100": EWMA(1.0 / 100.0)(dataset["air"]),
    }


dataset = xr.tutorial.open_dataset("air_temperature")
output, state = dataset.wax.stream().apply(
    my_custom_function, format_dims=dataset.air.dims
)

_ = output.isel(lat=0, lon=0).drop(["lat", "lon"]).to_pandas().plot(figsize=(12, 8))

You can see our Documentation for examples with EWMA or Binning on the air temperature dataset.

⚡ Performance on big dataframes ⚡

Check out our Documentation to see how you can use our "3-step workflow" to speed things up!

🔥 Speed 🔥

WAX-ML algorithms are implemented in JAX, so they are fast!

The use of JAX allows for leveraging hardware accelerators that optimize programs for the CPU, GPU, and TPU.

With WAX-ML, you can already compute an exponential moving average on a dataframe with 1 million rows with a 3x to 100x speedup (depending on the data container you use and speed measurement methodology) compared to pandas implementation. (See our notebook in the Quick Start Documentation or in Colaboratory ).

♻ Feedback loops ♻

Feedback is a fundamental notion in time-series analysis and has a wide history (see Feedback Wikipedia page for instance). So, we believe it is important to be able to implement them well in WAX-ML.

A fundamental piece in the implementation of feedback loops is the delay operator. We implement it with the delay module Lag which is itself implemented with the Buffer module, a module implementing the buffering mechanism.

The linear state-space models used to model linear time-invariant systems in signal theory are a well-known place where feedbacks are used to implement for instance infinite impulse response filters. This is easily implemented with the WAX-ML tools and will be implemented at a later time.

Another example is control theory or reinforcement learning. In reinforcement learning setup, an agent and an environment interact with a feedback loop. This generally results in a non-trivial global dynamic. In WAX-ML, we propose a simple module called GymFeedBack that allows the implementation of reinforcement learning experiments. This is built from an agent and an environment, both possibly having parameters and state:

• The agent is in charge of generating an action from observations.
• The environment is in charge of calculating a reward associated with the agent's action and preparing the next observation from some "raw observations" and the agent's action, which it gives back to the agent.

A feedback instance GymFeedback(agent, env) is a function that processes the "raw observations" and returns a reward as represented here:

Equivalently, we can describe the function GymFeedback(agent, env), after transformation by Haiku transformation, by a pair of pure functions init and apply that we describe here:

We have made concrete use of this feedback mechanism in this notebook where we give an example of online linear regression in a non-stationary environment:

• 🦎: online learning example , Open in Documentation 🦎

Here is an illustrative plot of the final result of the study:

• Left: The regret (cumulative sum of losses) first becomes concave, which means that the agent "learns something". Then, the regret curve has a bump at step 2000 where it becomes locally linear. It finally ends in a concave regime concave regime, which means that the agent has adapted to the new regime.
• Right: We see that the weights converge to the correct values in both regimes

Compatibility with other reinforcement learning frameworks

In addition, to ensure compatibility with other tools in the Gym ecosystem, we propose a transformation mechanism to transform functions into standard stateful Python objects following the Gym API for agents and environments implemented in deluca. These wrappers are in the wax.gym package.

WAX-ML implements callbacks in the wax.gym package. The callback API was inspired by the one in the one in dask.

WAX-ML should provide tools for reinforcement learning that should complement well those already existing such as RLax or deluca.

Future plans

Feedback loops and control theory

We would like to implement other types of feedback loops in WAX-ML. For instance, those of the standard control theory toolboxes, such as those implemented in the SLICOT SLICOT library.

Many algorithms in this space are absent from the Python ecosystem and we aim to provide JAX-based implementations and expose them with a simple API.

An idiomatic example in this field is the Kalman filter, a now-standard algorithm that dates back to the 1950s. After 30 years of existence, the Python ecosystem has still not integrated this algorithm into widely adopted libraries! Some implementations can be found in Python libraries such as python-control, stats-models, SciPy Cookbook. Also, some machine learning libraries have some closed and non-solved issues on this subject , see Scikit-learn#862 issue or River#355 issue. Why has the Kalman filter not found its place in these libraries? We think it may be because they have an object-oriented API, which makes them very well suited to the specific problems of modern machine learning but, on the other hand, prevents them from accommodating additional features such as Kalman filtering. We think the functional approach of WAX-ML, inherited from JAX, could well help to integrate a Kalman filter implementation in a machine learning ecosystem.

It turns out that Python code written with JAX is not very far from Fortran, a mathematical FORmula TRANslating system. It should therefore be quite easy and natural to reimplement standard algorithms implemented in Fortran, such as those in the SLICOT library with JAX. It seems that some questions about the integration of Fortran into JAX has already been raised. As noted in this discussion on JAX's Github page, it might even be possible to simply wrap Fortran code in JAX. This would avoid a painful rewriting process!

Along with the implementation of good old algorithms, we would like to implement more recent ones from the online learning literature that somehow revisits the filtering and control problems. In particular, we would like to implement the online learning version of the ARMA model developed in [3] and some online-learning versions of control theory algorithms, an approach called "the non-stochastic control problem", such as the linear quadratic regulator (see [4]).

Optimization

The JAX ecosystem already has a library dedicated to optimization: Optax, which we use in WAX-ML. We could complete it by offering other first-order algorithms such as the Alternating Direction Multiplier Method (ADMM). One can find "functional" implementations of proximal algorithms in libraries such as proxmin), ProximalOperators, or COSMO, which could give good reference implementations to start the work.

Another type of work took place around automatic differentiation and optimization. In [5] the authors implement differentiable layers based on convex optimization in the library cvxpylayers. They have implemented a JAX API but, at the moment, they cannot use the jit compilation of JAX yet (see this issue). We would be interested in helping to solve this issue.

Furthermore, in the recent paper [9], the authors propose a new efficient and modular implicit differentiation technique with a JAX-based implementation that should lead to a new open-source optimization library in the JAX ecosystem.

Other algorithms

The machine learning libraries Scikit-learn, River, ml-numpy implement many "traditional" machine learning algorithms that should provide an excellent basis for linking or reimplementing in JAX. WAX-ML could help to build a repository for JAX versions of these algorithms.

Other APIS

As it did for the Gym API, WAX-ML could add support for other high-level object-oriented APIs like Keras, Scikit-learn, River ...

Collaborations

The WAX-ML team is open to discussion and collaboration with contributors from any field who are interested in using WAX-ML for their problems on streaming data. We are looking for use cases around data streaming in audio processing, natural language processing, astrophysics, biology, finance, engineering ...

We believe that good software design, especially in the scientific domain, requires practical use cases and that the more diversified these use cases are, the more the developed functionalities will be guaranteed to be well implemented.

By making this software public, we hope to find enthusiasts who aim to develop WAX-ML further!

⚒ Installation ⚒

You can install WAX-ML with the command:

pip install wax-ml

To install the latest version from source, you can use the command :

pip install "wax-ml[dev,complete] @ git+https://github.com/eserie/wax-ml.git"

Disclaimer

WAX-ML is in its early stages of development and its features and API are very likely to evolve.

Development

You can contribute to WAX-ML by asking questions, proposing practical use cases, or by contributing to the code or the documentation. You can have a look at our Contributing Guidelines and Developer Documentation .

We maintain a "WAX-ML Enhancement Proposals" in WEP.md file.

References

[1] Google Princeton AI and Hazan Lab @ Princeton University

[2] FNet: Mixing Tokens with Fourier Transforms, James Lee-Thorp, Joshua Ainslie, Ilya Eckstein, Santiago Ontanon

[3] Online Learning for Time Series Prediction, Oren Anava, Elad Hazan, Shie Mannor, Ohad Shamir

[4] The Nonstochastic Control Problem, Elad Hazan, Sham M. Kakade, Karan Singh

[5] Differentiable Convex Optimization Layers, Akshay Agrawal, Brandon Amos, Shane Barratt, Stephen Boyd, Steven Diamond, Zico Kolter

[6] Machine learning accelerated computational fluid dynamics, Dmitrii Kochkov, Jamie A. Smith, Ayya Alieva, Qing Wang, Michael P. Brenner, Stephan Hoyer

[7] Large dimension forecasting models and random singular value spectra, Jean-Philippe Bouchaud, Laurent Laloux, M. Augusta Miceli, Marc Potters

[8] A novel dynamic PCA algorithm for dynamic data modeling and process monitoring, Yining Dongac and S. JoeQina

[9] Efficient and Modular Implicit Differentiation, Mathieu Blondel, Quentin Berthet, Marco Cuturi, Roy Frostig, Stephan Hoyer, Felipe Llinares-López, Fabian Pedregosa, Jean-Philippe Vert

License

Copyright 2021 The WAX-ML Authors

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    https://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

WAX-ML bundles portions of astropy, dask, deluca, haiku, jax, xarray.

astropy, dask are available under a "3-clause BSD" license:

• dask: wax/gym/callbacks/callbacks.py
• astropy: CONTRIBUTING.md

deluca, haiku, jax and xarray are available under a "Apache" license:

• deluca: wax/gym/entity.py
• haiku: docs/notebooks/05_reconstructing_the_light_curve_of_stars.*
• jax: docs/conf.py, docs/developer.md
• xarray: wax/datasets/generate_temperature_data.py

The full text of these licenses is included in the licenses directory.

Citing WAX-ML

If you use WAX-ML, please cite our paper using the BibTex entry:

@misc{sérié2021waxml,
      title={{WAX-ML}: {A} {P}ython library for machine learning and feedback loops on streaming data},
      author={Emmanuel Sérié},
      year={2021},
      eprint={2106.06524},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url = {http://arxiv.org/abs/2106.06524},
}

Reference documentation

For details about the WAX-ML API, see the reference documentation.