Meta AI & ML Strategy Questions

import numpy as np
from math import log
from scipy import stats

def _freedman_diaconis_bins(data, max_bins=200):
    # Robust bin width estimator
    q75, q25 = np.percentile(data, [75, 25])
    iqr = q75 - q25
    if iqr == 0:
        return min(max_bins, 50)
    bw = 2 * iqr * (len(data) ** (-1/3))
    if bw <= 0:
        return min(max_bins, 50)
    bins = int(np.clip(np.ceil((data.max() - data.min()) / bw), 10, max_bins))
    return bins

def _js_divergence(p, q, base=np.e):
    # p, q are probability vectors (sum to 1)
    m = 0.5 * (p + q)
    # add tiny eps to avoid log(0)
    eps = 1e-12
    p = np.clip(p, eps, 1)
    q = np.clip(q, eps, 1)
    m = np.clip(m, eps, 1)
    return 0.5 * (np.sum(p * np.log(p / m) / log(base)) + np.sum(q * np.log(q / m) / log(base)))

def detect_drift(reference_samples, recent_samples, method='ks', threshold=0.1, max_samples=100000):
    """
    Returns (score, drift_bool).
    - method: 'ks' uses Kolmogorov-Smirnov D statistic (0..1).
              'js' uses normalized Jensen-Shannon (0..1).
    - threshold: decision threshold on returned score (higher => more drift).
    - max_samples: cap per array for performance (deterministic downsample via slicing).
    """
    ref = np.asarray(reference_samples, dtype=float)
    rec = np.asarray(recent_samples, dtype=float)
    # quick checks
    if ref.size == 0 or rec.size == 0:
        raise ValueError("reference_samples and recent_samples must be non-empty")
    # deterministic subsample if needed
    if ref.size > max_samples:
        step = max(1, ref.size // max_samples)
        ref = ref[::step][:max_samples]
    if rec.size > max_samples:
        step = max(1, rec.size // max_samples)
        rec = rec[::step][:max_samples]

    if method == 'ks':
        # use scipy two-sample KS; return D statistic as score
        D, pvalue = stats.ks_2samp(ref, rec, alternative='two-sided', mode='asymp')
        score = float(D)  # between 0 and 1
    elif method == 'js':
        # histogram-based JS divergence
        combined = np.concatenate([ref, rec])
        bins = _freedman_diaconis_bins(combined, max_bins=200)
        hist_ref, edges = np.histogram(ref, bins=bins, density=False)
        hist_rec, _ = np.histogram(rec, bins=edges, density=False)
        p = hist_ref / hist_ref.sum()
        q = hist_rec / hist_rec.sum()
        # compute JS divergence with natural log; max JS = ln(2)
        js = _js_divergence(p, q, base=np.e)
        # normalize to [0,1] by dividing by ln(2) then take sqrt to make it more comparable to KS scale
        score = float(np.sqrt(js / log(2)))
        score = min(max(score, 0.0), 1.0)
    else:
        raise ValueError("Unsupported method. Choose 'ks' or 'js'.")

    drift = score >= threshold
    return score, drift