BLS/NNLS (Bounded/Non-Negative Least Squares)

Bounded Least Squares and Non-Negative Least Squares for constrained optimization.

Functions

Function	Type	Description
bls_fit_agg	Aggregate	Bounded Least Squares with box constraints
nnls_fit_agg	Aggregate	Non-Negative Least Squares (coefficients >= 0)
bls_fit_predict_agg	Aggregate	Fit and predict with GROUP BY support
bls_fit_predict_by	Table Macro	Per-group regression with long-format output

anofox_stats_bls_fit_agg

Bounded Least Squares with box constraints on coefficients.

Signature:

anofox_stats_bls_fit_agg(
    y DOUBLE,
    x LIST(DOUBLE),
    [options MAP]
) -> STRUCT

Options MAP:

Key	Type	Default	Description
fit_intercept	BOOLEAN	false	Include intercept term
lower_bound	DOUBLE	-	Lower bound for all coefficients
upper_bound	DOUBLE	-	Upper bound for all coefficients
max_iterations	INTEGER	1000	Maximum iterations
tolerance	DOUBLE	1e-10	Convergence tolerance

Returns: BlsFitResult STRUCT

Example:

-- Coefficients bounded between 0 and 1
SELECT bls_fit_agg(
    y,
    [x1, x2, x3],
    {'lower_bound': 0.0, 'upper_bound': 1.0}
)
FROM portfolio_data;

-- Only lower bound (coefficients >= 0)
SELECT bls_fit_agg(
    y,
    [x1, x2],
    {'lower_bound': 0.0}
)
FROM data;

anofox_stats_nnls_fit_agg

Non-Negative Least Squares - all coefficients constrained to be >= 0.

Signature:

anofox_stats_nnls_fit_agg(
    y DOUBLE,
    x LIST(DOUBLE),
    [options MAP]
) -> STRUCT

Options MAP:

Key	Type	Default	Description
fit_intercept	BOOLEAN	false	Include intercept term
max_iterations	INTEGER	1000	Maximum iterations
tolerance	DOUBLE	1e-10	Convergence tolerance

Returns: BlsFitResult STRUCT

Example:

-- Non-negative coefficients (e.g., mixture models)
SELECT nnls_fit_agg(spectrum, [component1, component2, component3])
FROM spectral_data;

-- Portfolio weights (no short selling)
SELECT nnls_fit_agg(returns, [stock1, stock2, stock3])
FROM portfolio_data;

-- Per-group NNLS
SELECT
    category,
    (nnls_fit_agg(y, [x1, x2])).coefficients
FROM data
GROUP BY category;

Use Cases

• Spectral unmixing / mixture models: Component proportions must be non-negative
• Portfolio optimization: No short selling constraint
• Physical constraints: Concentrations, weights must be positive
• Image processing: Non-negative matrix factorization
• Signal processing: Source separation

See Also

• OLS - Unconstrained regression
• Ridge - Regularized regression
• Table Macros - Per-group predictions