commit 54282d253042a7ec1891ef4fe72496f4908ffa52
parent 18a95aecce2a74ea6abd7b1a62adf07c927e4a9c
Author: Jared Tobin <jared@jtobin.io>
Date: Sat, 4 Jul 2026 16:27:06 -0230
fix: uncap the ConfSeq plug-in bet
Numeric.Eproc.ConfSeq pre-capped the shared predictable plug-in bet
at the truncation level c = 1/2 before applying the candidate-
specific truncations c/m and c/(1 - m). Since both exceed c on the
interior grid, those truncations could never bind: a conservative
deviation from the WSR (2024) eq. (26) bet that Theorem 3 and the
module documentation describe, slowing rejection of extreme
candidates early in the stream.
Drop the pre-cap. The raw eq. (26) bet is now truncated only per-
candidate, restoring the paper's construction and its early power;
every capital factor retains the 1 - c floor via the truncations
themselves, so coverage is unaffected. The update haddock, which
carried the same pre-cap in its bet formula, and the module-header
example output are corrected to match.
Validated with and without -f+llvm.
Diffstat:
1 file changed, 7 insertions(+), 7 deletions(-)
diff --git a/lib/Numeric/Eproc/ConfSeq.hs b/lib/Numeric/Eproc/ConfSeq.hs
@@ -69,7 +69,7 @@
-- >>> let Right cfg = config 0.0 1.0 0.05 100
-- >>> let xs = concat (replicate 50 [1, 1, 0, 1, 1, 0, 1, 1, 1, 1])
-- >>> interval cfg (foldl' (update cfg) (initial cfg) xs)
--- Just (0.7326732673267327,0.8514851485148515)
+-- Just (0.7326732673267327,0.8613861386138614)
module Numeric.Eproc.ConfSeq (
-- * Confidence-sequence configuration and state
@@ -218,14 +218,15 @@ initial Config{..} = State {
-- plug-in bet from the statistics accumulated through the
-- /previous/ step (Waudby-Smith & Ramdas (2024), eq. (26)):
--
--- @lambda_t = min c (sqrt (2 log(2 \/ alpha)
--- \/ (sigma^2_{t-1} * t * log(1 + t))))@
+-- @lambda_t = sqrt (2 log(2 \/ alpha)
+-- \/ (sigma^2_{t-1} * t * log(1 + t)))@
--
--- with @c = 1\/2@. The bet is computed once and shared across all
+-- The bet is computed once and shared across all
-- live candidates -- its independence from @m@ is what keeps the
-- survivor set an interval. Each live candidate @m@ then updates
-- its pair of log-capitals with the truncated bets
--- @min lambda_t (c \/ m)@ and @min lambda_t (c \/ (1 - m))@, and
+-- @min lambda_t (c \/ m)@ and @min lambda_t (c \/ (1 - m))@,
+-- with @c = 1\/2@, and
-- is dropped iff @max(log K^+, log K^-)@ has reached
-- @log(2 \/ alpha)@. Finally @y@ is folded into the shared
-- statistics, preserving predictability of the next bet.
@@ -245,8 +246,7 @@ update Config{..} State{..} !x =
!gp1 = fromIntegral (cfg_grid + 1)
-- sigma^2_{t-1} = (1/4 + sum_{i<=t-1} (y_i - mu_i)^2) / t
!sig2 = (0.25 + st_sum_dev2) / td
- !lam = min trunc_c
- (sqrt (cfg_bet_num / (sig2 * td * log1p td)))
+ !lam = sqrt (cfg_bet_num / (sig2 * td * log1p td))
-- built eagerly, as in 'initial': the tail is forced before
-- consing, so the new live list is in normal form on
-- construction.
