Fastest way for 2D rolling window quantile?

Question

I want to calculate a rolling quantile of a large 2D matrix with dimensions (1e6, 1e5), column wise. I am looking for the fastest way, since I need to perform this operation thousands of times, and it's very computationally expensive. For experiments window=1000 and q=0.1 is used.

import numpy as np
import pandas as pd
import multiprocessing as mp
from functools import partial
import numba as nb
X = np.random.random((10000,1000)) # Original array has dimensions of about (1e6, 1e5)

My current approaches:

Pandas: %timeit: 5.8 s ± 15.5 ms per loop

def pd_rolling_quantile(X, window, q):
    return pd.DataFrame(X).rolling(window).quantile(quantile=q)

Numpy Strided: %timeit: 2min 42s ± 3.29 s per loop

def strided_app(a, L, S):
    nrows = ((a.size-L)//S)+1
    n = a.strides[0]
    return np.lib.stride_tricks.as_strided(a, shape=(nrows,L), strides=(S*n,n))
def np_1d(x, window, q):
    return np.pad(np.percentile(strided_app(x, window, 1), q*100, axis=-1), (window-1, 0) , mode='constant')
def np_rolling_quantile(X, window, q):
    results = []
    for i in np.arange(X.shape[1]):
        results.append(np_1d(X[:,i], window, q))
    return np.column_stack(results)

Multiprocessing: %timeit: 1.13 s ± 27.6 ms per loop

def mp_rolling_quantile(X, window, q):
    pool = mp.Pool(processes=12)
    results = pool.map(partial(pd_rolling_quantile, window=window, q=q), [X[:,i] for i in np.arange(X.shape[1])])
    pool.close()
    pool.join()
    return np.column_stack(results)

Numba: %timeit: 2min 28s ± 182 ms per loop

@nb.njit
def nb_1d(x, window, q):
    out = np.zeros(x.shape[0])
    for i in np.arange(x.shape[0]-window+1)+window:
        out[i-1] = np.quantile(x[i-window:i], q=q)
    return out
def nb_rolling_quantile(X, window, q):
    results = []
    for i in np.arange(X.shape[1]):
        results.append(nb_1d(X[:,i], window, q))
    return np.column_stack(results)

The timings are not great, and ideally I would target an improvement of 10-50x by speed. I would appreciate any suggestions, how to speed it up. Maybe someone has ideas on using lower level languages (Cython), or other ways to speed it up with Numpy/Numba/Tensorflow based methods. Thanks!

Answer 1

I would recommend the new rolling-quantiles package. To demonstrate, even the somewhat naive approach of constructing a separate filter for each column outperforms the above single-threaded pandas experiment:

pipes = [rq.Pipeline(rq.LowPass(window=1000, quantile=0.1)) for i in range(1000)]
%timeit [pipe.feed(X[:, i]) for i, pipe in enumerate(pipes)]
1.34 s ± 7.76 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

versus

df = pd.DataFrame(X)
%timeit df.rolling(1000).quantile(0.1)
5.63 s ± 27 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

Both can be trivially parallelized by means of multiprocessing, as you showed.