Expectation.h File Reference

Analytical expectation / variance / moment evaluator over RV circuits. More...

#include <optional>
#include "GenericCircuit.h"

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Namespaces
namespace	provsql

Functions
double	provsql::compute_expectation (const GenericCircuit &gc, gate_t root, std::optional< gate_t > event_root=std::nullopt)
	Compute \(E[X]\) (or \(E[X \mid A]\) if event_root is set) over the scalar sub-circuit rooted at root.
double	provsql::compute_variance (const GenericCircuit &gc, gate_t root, std::optional< gate_t > event_root=std::nullopt)
	Compute \(\mathrm{Var}[X]\) (or \(\mathrm{Var}[X \mid A]\) if event_root is set) over the scalar sub-circuit rooted at root.
double	provsql::compute_raw_moment (const GenericCircuit &gc, gate_t root, unsigned k, std::optional< gate_t > event_root=std::nullopt)
	Compute the raw moment \(E[X^k]\) (or \(E[X^k \mid A]\) if event_root is set) for k >= 0.
double	provsql::compute_central_moment (const GenericCircuit &gc, gate_t root, unsigned k, std::optional< gate_t > event_root=std::nullopt)
	Compute the central moment \(E[(X - E[X])^k]\) (or \(E[(X - E[X \mid A])^k \mid A]\) if event_root is set).
double	provsql::evaluateBooleanProbability (const GenericCircuit &gc, gate_t boolRoot)
	Probability that the Boolean subcircuit rooted at boolRoot evaluates to true under the tuple-independent probabilistic-database model.

Detailed Description

Analytical expectation / variance / moment evaluator over RV circuits.

Computes E[X], Var[X], raw moments E[X^k] and central moments E[(X - E[X])^k] over a sub-circuit rooted at a scalar gate (gate_value, gate_rv, or gate_arith), using closed-form formulas wherever the sub-DAG decomposes structurally and falling back to Monte Carlo (via monteCarloScalarSamples) when structural shortcuts cannot decide a sub-expression.

Decomposition rules:

• gate_value: literal, constant moments.
• gate_rv: closed-form moments per RandomVariable.h.
• gate_arith PLUS / MINUS / NEG: linearity of expectation always applies; variance and higher moments require structural independence of the children (their reachable gate_rv footprints must be pairwise disjoint).
• gate_arith TIMES: requires structural independence; otherwise MC fallback.
• gate_arith DIV: closed form when the divisor is a deterministic constant (gate_value), otherwise MC fallback.

MC fallback is governed by the provsql.rv_mc_samples GUC: non-zero values pick the sample count; zero disables the fallback, causing the evaluator to throw rather than sample. This keeps a single knob shared with future RV-MC fallback paths (Priority 7's island decomposer).

Definition in file Expectation.h.