Metadata-Version: 2.4
Name: diffcb
Version: 0.1.6
Summary: Differentiable Critical Bandwidth: Silverman's modality test as a differentiable PyTorch layer with IFT backward pass.
Project-URL: Homepage, https://github.com/ryZhangHason/differentiable-critical-bandwidth
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Project-URL: Bug Tracker, https://github.com/ryZhangHason/differentiable-critical-bandwidth/issues
Author-email: Ruiyu Zhang <dhhhason@gmail.com>
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License-File: LICENSE
Keywords: PyTorch,anomaly detection,critical bandwidth,differentiable programming,generative models,kernel density estimation,mode counting,nonparametric statistics
Classifier: Development Status :: 3 - Alpha
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: Apache Software License
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.9
Classifier: Programming Language :: Python :: 3.10
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Classifier: Topic :: Scientific/Engineering :: Artificial Intelligence
Classifier: Topic :: Scientific/Engineering :: Mathematics
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Description-Content-Type: text/markdown

# DCB — Differentiable Critical Bandwidth

[![PyPI](https://img.shields.io/pypi/v/diffcb.svg)](https://pypi.org/project/diffcb/)
[![License: Apache 2.0](https://img.shields.io/badge/License-Apache%202.0-blue.svg)](LICENSE)
[![Python 3.9+](https://img.shields.io/badge/python-3.9+-blue.svg)](https://www.python.org/)

A PyTorch package that makes **Silverman's critical bandwidth test (1981)** fully differentiable, enabling end-to-end gradient-based optimization over the modal structure of continuous distributions.

## Overview

The critical bandwidth `h_crit` is the minimum KDE bandwidth at which a distribution appears to have at most `m` modes — a classical nonparametric statistic for modality testing. DCB replaces every non-differentiable operation in its computation with a smooth surrogate, then uses the **Implicit Function Theorem** to compute exact gradients through the root-finding step at O(1) memory cost.

```python
import torch
from dcb import DCBLayer

X = torch.randn(1000, requires_grad=True)   # 1D samples
layer = DCBLayer(target_modes=1)
h_crit = layer(X)                           # differentiable scalar
h_crit.backward()                           # exact IFT gradients
```

## Installation

```bash
pip install diffcb
```

Or from source:

```bash
git clone https://github.com/ryZhangHason/differentiable-critical-bandwidth
cd differentiable-critical-bandwidth
pip install -e ".[dev]"
```

## Accuracy vs R's `bw.crit`

DCB is validated against R's `multimode::bw.crit(data, mod0=1)` — the standard reference implementation of Hall & York (2001). On **identical data**:

| n | DCB vs R (same sample) | DCB vs R (independent samples) |
|---|---|---|
| 100K | **0.004%** | ~0.5% (MC noise from independent RNG) |
| 1M | **0.005%** | ~0.2% |
| 10M | **0.004%** | ~0.1% |

The independent-sample figures reflect natural sampling variability (two unbiased estimators drawing different data), not algorithmic error. On identical data, DCB agrees with R to within **0.005%** at all tested n. DCB is 43× faster than R at n=100M (1.1 s vs 50 s) and handles n=2B in 24 s while R OOMs.

## Key Parameters

```python
DCBLayer(
    target_modes=1,       # target number of modes
    G=512,                # IFT evaluation grid points
    use_fft=True,         # FFT forward (default); eliminates subsampling bias for n>50K
    max_n_exact=1_000_000,# sketch to sketch_size when n exceeds this (None = always exact)
    sketch_size=500_000,  # sketch target; 500K matches full-n accuracy (O(n^{-2/9}) rate)
    safe_backward=False,  # clamp IFT denominator near bifurcations
)
```

## Confirmed Experimental Results

All GPU results produced on Kaggle (T4 / P100) — see `experiments/` and `outputs/`.

| Experiment | Result | Criterion |
|---|---|---|
| **Accuracy vs R (same data, n=100K)** | **0.004%** | < 0.01% ✓ |
| **Validation (m≥2, Marron-Wand)** | R²=0.91, MAE=0.07, ρ=0.89 | R²≥0.85 ✓ |
| **Speedup vs scipy (CUDA T4, n=8192)** | **10.5×** | ≥3× ✓ |
| **GAN mode preservation** | h_crit=1.232 >> 0.3 | h_crit>0.3 ✓ |
| **Anomaly AUC (KDDCup99)** | DCB=**0.9982** vs IF=0.9867 | DCB≥IF ✓ |

## Repository Structure

```
dcb/            Core PyTorch package
  layer.py        DCBLayer nn.Module + DCBFunction autograd
  solver.py       IFT root-finder and backward pass
  fft_kde.py      FFT-based mode counter (MPS-safe, float64, G=16384)
  kde.py          Direct KDE derivatives (small-n path)
  utils.py        Grid, Silverman bandwidth, sg() stabilizer
experiments/    Reproduction scripts for all paper figures and tables
  phase1_*.py     Validation, speedup, ablation (Figures 1–2, S1–S2)
  phase2_gan.py   GAN mode-collapse prevention (Figure 3)
  phase3_anomaly.py  Anomaly detection (Table 2, Figure 5)
  round20_*.py    Large-n R comparison and streaming benchmarks
  round21_*.py    Accuracy improvement experiments
tests/          Unit tests (pytest, 45 passed, 1 xfailed)
outputs/        All generated figures and tables (PDFs, PNGs, CSVs)
```

## License

Apache 2.0 — see [LICENSE](LICENSE).
