perf: chan's parallel mean-var algorithm for dask

benchmarks/asv.conf.json

@@ -84,6 +84,7 @@
         "pooch": [""],
         "scikit-image": [""], // https://github.com/conda-forge/scikit-misc-feedstock/pull/29
         // "scikit-misc": [""],
+        "dask": [""],
     },
 
     // Combinations of libraries/python versions can be excluded/included

benchmarks/benchmarks/preprocessing_counts.py

@@ -10,6 +10,7 @@
 from typing import TYPE_CHECKING
 
 import anndata as ad
+import zarr
 
 import scanpy as sc
 from scanpy._utils import get_literal_vals
@@ -151,17 +152,34 @@ def peakmem_log1p(self, *_) -> None:
 
 
 class Agg:  # noqa: D101
-    params: tuple[AggType] = tuple(get_literal_vals(AggType))
-    param_names = ("agg_name",)
+    params: tuple[list[str], list[bool]] = (
+        list(get_literal_vals(AggType)),
+        [True, False],
+    )
+    param_names = ("agg_name", "use_dask")
 
     def setup_cache(self) -> None:
         """Without this caching, asv was running several processes which meant the data was repeatedly downloaded."""
         adata, _ = get_dataset("lung93k")
-        adata.write_h5ad("lung93k.h5ad")
-
-    def setup(self, agg_name: AggType) -> None:
-        self.adata = ad.read_h5ad("lung93k.h5ad")
-        self.agg_name = agg_name
+        adata.write_zarr("lung93k.zarr")
+
+    def setup(self, agg_name: AggType, use_dask: bool) -> None:  # noqa: FBT001
+        if use_dask:
+            if agg_name == "median":
+                # Skip this one: https://asv.readthedocs.io/en/stable/writing_benchmarks.html#setup-and-teardown-functions
+                raise NotImplementedError()
+            z = zarr.open("lung93k.zarr")
+            self.adata = ad.AnnData(
+                obs=ad.io.read_elem(z["obs"]),
+                var=ad.io.read_elem(z["var"]),
+                layers={
+                    "counts": ad.experimental.read_elem_lazy(z["layers"]["counts"])
+                },
+                X=ad.experimental.read_elem_lazy(z["X"]),
+            )
+        else:
+            self.adata = ad.read_zarr("lung93k.zarr")
+        self.agg_name: AggType = agg_name
 
     def time_agg(self, *_) -> None:
         sc.get.aggregate(

src/scanpy/get/_aggregated.py

@@ -6,7 +6,6 @@
 import numpy as np
 import pandas as pd
 from anndata import AnnData
-from fast_array_utils.stats._power import power as fau_power  # TODO: upstream
 from scipy import sparse
 from sklearn.utils.sparsefuncs import csc_median_axis_0
 
@@ -371,16 +370,129 @@ def aggregate_dask_mean_var(
     mask: NDArray[np.bool] | None = None,
     dof: int = 1,
 ) -> MeanVarDict:
-    mean = aggregate_dask(data, by, "mean", mask=mask, dof=dof)["mean"]
-    sq_mean = aggregate_dask(fau_power(data, 2), by, "mean", mask=mask, dof=dof)["mean"]
-    # TODO: If we don't compute here, the results are not deterministic under the process cluster for sparse.
-    if isinstance(data._meta, CSRBase):
-        sq_mean = sq_mean.compute()
-    var = sq_mean - fau_power(mean, 2)
-    if dof != 0:
-        group_counts = np.bincount(by.codes)
-        var *= (group_counts / (group_counts - dof))[:, np.newaxis]
-    return MeanVarDict(mean=mean, var=var)
+    """Compute group-wise mean and variance for a dask array.
+
+    Per chunk we compute ``(count, mean, M2)`` (where ``M2 = sum((x - mean)**2)``),
+    then combine across chunks with the pairwise parallel algorithm from
+    Chan et al. (https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Parallel_algorithm)
+    so the across-chunk reduction avoids the catastrophic cancellation of
+    ``E[X**2] - E[X]**2``.
+    """
+    import dask.array as da
+
+    n_categories = len(by.categories)
+    n_features = data.shape[1]
+    chunked_axis = 0 if isinstance(data._meta, CSRBase | np.ndarray) else 1
+
+    if chunked_axis == 1:
+        # Each block already sees every observation, so mean/var per chunk is final.
+        def per_block_col(chunk: Array) -> NDArray[np.float64]:
+            mean_, var_ = Aggregate(groupby=by, data=chunk, mask=mask).mean_var(dof=dof)
+            return np.concatenate([mean_, var_], axis=0)
+
+        combined = data.map_blocks(
+            per_block_col,
+            chunks=((2 * n_categories,), data.chunks[1]),
+            meta=np.array([], dtype=np.float64),
+        )
+        return MeanVarDict(mean=combined[:n_categories], var=combined[n_categories:])
+
+    n_blocks = data.numblocks[0]
+
+    def per_block_row(
+        chunk: Array, block_info: dict | None = None
+    ) -> NDArray[np.float64]:
+        row_subset = slice(*block_info[0]["array-location"][0])
+        by_sub = by[row_subset]
+        mask_sub = mask[row_subset] if mask is not None else None
+        return _block_moments(chunk, by_sub, mask=mask_sub, n_categories=n_categories)[
+            None
+        ]
+
+    per_block_stats = data.map_blocks(
+        per_block_row,
+        chunks=((1,) * n_blocks, (3,), (n_categories,), (n_features,)),
+        new_axis=(1, 2),
+        meta=np.array([], dtype=np.float64),
+    )
+
+    combined = da.reduction(
+        per_block_stats,
+        chunk=lambda x, axis=None, keepdims=False: x,
+        aggregate=_chan_reduce_axis_0,
+        axis=0,
+        keepdims=False,
+        concatenate=True,
+        dtype=np.float64,
+        meta=np.array([], dtype=np.float64),
+    )
+    counts = combined[0]
+    mean_ = combined[1]
+    m2 = combined[2]
+    denom = counts - dof if dof > 0 else counts
+    return MeanVarDict(mean=mean_, var=m2 / denom)
+
+
+def _block_moments(
+    data: np.ndarray | CSBase,
+    by: pd.Categorical,
+    *,
+    mask: NDArray[np.bool] | None,
+    n_categories: int,
+) -> NDArray[np.float64]:
+    """Per-chunk ``(count, mean, M2)`` array of shape ``(3, n_categories, n_features)``.
+
+    Groups with no observations in the chunk get zeros for mean and M2 so
+    they combine cleanly under ``_chan_combine``.
+    """
+    codes = by.codes
+    valid = codes >= 0
+    if mask is not None:
+        valid = valid & mask
+    counts = np.bincount(codes[valid], minlength=n_categories).astype(np.float64)
+
+    out = np.zeros((3, n_categories, data.shape[1]), dtype=np.float64)
+    out[0] = counts[:, None]
+    nonempty = counts > 0
+    if not nonempty.any():
+        return out
+
+    agg = Aggregate(groupby=by, data=data, mask=mask)
+    sum_ = agg.sum()
+    sum_sq = agg._sum(_power(data, 2))
+    safe_counts = np.where(nonempty, counts, 1)[:, None]
+    mean_ = sum_ / safe_counts
+    # M2 = sum((x - mean)**2) = sum_sq - count * mean**2; clip cancellation noise to 0.
+    m2 = np.maximum(sum_sq - sum_ * mean_, 0)
+    out[1, nonempty] = mean_[nonempty]
+    out[2, nonempty] = m2[nonempty]
+    return out
+
+
+def _chan_combine(
+    a: NDArray[np.float64], b: NDArray[np.float64]
+) -> NDArray[np.float64]:
+    """Combine two ``(3, K, F)`` ``(count, mean, M2)`` stat blocks pairwise."""
+    n_a, mean_a, m2_a = a[0], a[1], a[2]
+    n_b, mean_b, m2_b = b[0], b[1], b[2]
+    n = n_a + n_b
+    safe_n = np.where(n > 0, n, 1)
+    delta = mean_b - mean_a
+    new_mean = mean_a + delta * n_b / safe_n
+    new_m2 = m2_a + m2_b + delta * delta * n_a * n_b / safe_n
+    return np.stack([n, new_mean, new_m2])
+
+
+def _chan_reduce_axis_0(
+    stats: NDArray[np.float64],
+    axis: int | None,
+    keepdims: bool,  # noqa: FBT001
+) -> NDArray[np.float64]:
+    """Aggregate per-block stats along axis 0 with the parallel variance algorithm."""
+    result = stats[0]
+    for i in range(1, stats.shape[0]):
+        result = _chan_combine(result, stats[i])
+    return result[None] if keepdims else result
 
 
 @_aggregate.register(DaskArray)