riantr/moonbit_dowhy/utils

README
- ::causal_graphCausalModel::causal_graph
- ::dataCausalModel::data
- ::estimate_effectCausalModel::estimate_effect
- ::identified_estimandCausalModel::identified_estimand
- ::identify_effectCausalModel::identify_effect
- ::newCausalModel::new
- ::refute_estimateCausalModel::refute_estimate

riantr/moonbit_dowhy/utils does not have a README file

GlmFamily

pub enum GlmFamily {
  Gaussian
  Binomial
  Poisson
}

The response distribution of a generalised linear model.

GlmFamily::binomial

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fn GlmFamily::binomial() -> GlmFamily

The binomial family, with the logit link.

GlmFamily::gaussian

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fn GlmFamily::gaussian() -> GlmFamily

The normal family, with the identity link.

GlmFamily::name

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fn GlmFamily::name(self : GlmFamily) -> String

The name of a generalised linear model family.

GlmFamily::poisson

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fn GlmFamily::poisson() -> GlmFamily

The poisson family, with the log link.

GlmFit

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pub struct GlmFit {
  beta : Array[Double]
  mu : Array[Double]
  eta : Array[Double]
  cov : Matrix
  se : Array[Double]
  iterations : Int
  converged : Bool
  family : GlmFamily
}

The result of a generalised linear model fit.

GlmFit::empty

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fn GlmFit::empty() -> GlmFit

A generalised linear model without any data.

LogisticFit

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pub struct LogisticFit {
  beta : Array[Double]
  iterations : Int
  converged : Bool
}

Result of a logistic regression fit.

Matrix

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pub struct Matrix {
  rows : Int
  cols : Int
  data : Array[Double]
}

Dense row-major matrix used by the estimation routines.

This mirrors the small subset of numpy that the DoWhy estimators rely on: a design matrix is built from a data frame, a model is fitted against a response vector and the fitted coefficients / standard errors are read back.

Matrix::col

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fn Matrix::col(self : Matrix, j : Int) -> Array[Double]

Column j as an array.

Matrix::copy

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fn Matrix::copy(self : Matrix) -> Matrix

A copy of the matrix.

Matrix::from_columns

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fn Matrix::from_columns(columns : Array[Array[Double]]) -> Matrix

Build a matrix whose rows are the given vectors.

Matrix::from_flat

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fn Matrix::from_flat(rows : Int, cols : Int, data : Array[Double]) -> Matrix

Build a matrix from a flat array in row-major order.

Matrix::from_rows

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fn Matrix::from_rows(rows : Array[Array[Double]]) -> Matrix

Build a matrix from a list of rows.

Matrix::get

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fn Matrix::get(self : Matrix, i : Int, j : Int) -> Double

Element access.

Matrix::identity

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fn Matrix::identity(n : Int) -> Matrix

Build the identity matrix of size n.

Matrix::matvec

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fn Matrix::matvec(self : Matrix, v : Array[Double]) -> Array[Double]

Matrix-vector product self * v.

Matrix::matvec_t

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fn Matrix::matvec_t(self : Matrix, v : Array[Double]) -> Array[Double]

Transpose-vector product self^T * v.

Matrix::mul

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fn Matrix::mul(self : Matrix, other : Matrix) -> Matrix

Matrix product self * other.

Matrix::mul_t

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fn Matrix::mul_t(self : Matrix, other : Matrix) -> Matrix

self^T * other.

Matrix::ncols

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fn Matrix::ncols(self : Matrix) -> Int

Number of columns.

Matrix::nrows

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fn Matrix::nrows(self : Matrix) -> Int

Number of rows.

Matrix::row

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fn Matrix::row(self : Matrix, i : Int) -> Array[Double]

Row i as an array.

Matrix::set

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fn Matrix::set(self : Matrix, i : Int, j : Int, v : Double) -> Unit

Element assignment.

Matrix::transpose

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fn Matrix::transpose(self : Matrix) -> Matrix

Transpose of the matrix.

Matrix::zeros

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fn Matrix::zeros(rows : Int, cols : Int) -> Matrix

Build a zero filled matrix of the given shape.

OlsFit

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pub struct OlsFit {
  beta : Array[Double]
  fitted : Array[Double]
  residuals : Array[Double]
  rss : Double
  n : Int
  rank : Int
  df_resid : Int
  sigma2 : Double
  cov : Matrix
  se : Array[Double]
  tstat : Array[Double]
}

Result of an ordinary least squares fit.

OlsFit::empty

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fn OlsFit::empty() -> OlsFit

An ordinary least squares fit without any data.

Random

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pub struct Random {
  state : UInt64
}

A small deterministic pseudo random generator.

The refuters need reproducible randomness, so the port carries its own generator instead of relying on the platform entropy of the toolchain. It is a 64 bit xorshift, which is enough for the resampling and the noise the refuters add.

Random::new

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fn Random::new(seed : UInt64) -> Random

A generator with the given seed.

Random::next_double

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fn Random::next_double(self : Random) -> Double

The next value in [0, 1).

Random::next_int

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fn Random::next_int(self : Random, bound : Int) -> Int

The next value in [0, bound).

Random::next_normal

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fn Random::next_normal(self : Random) -> Double

The next value from the standard normal distribution.

Box-Muller transform; the second variate is discarded.

Random::next_u64

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fn Random::next_u64(self : Random) -> UInt64

The next raw 64 bit value.

Random::sample_with_replacement

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fn Random::sample_with_replacement(self : Random, values : Array[Double], size : Int) -> Array[Double]

A sample of size values drawn with replacement.

Random::shuffle

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fn Random::shuffle(self : Random, values : Array[Double]) -> Array[Double]

A random permutation of the given values.

average_rank

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fn average_rank(values : Array[Double]) -> Array[Double]

Average ranks of the values, matching pandas.Series.rank(ascending=True).

Tied values receive the mean of the ranks they span.

betainc

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fn betainc(a : Double, b : Double, x : Double) -> Double

Regularised incomplete beta function I_x(a, b).

chi2_cdf

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fn chi2_cdf(x : Double, df : Double) -> Double

The cumulative distribution function of the chi-square distribution.

chi2_ppf

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fn chi2_ppf(p : Double, df : Double) -> Double

The quantile function of the chi-square distribution.

The quantile p is the x for which the distribution function is p.

chi2_sf

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fn chi2_sf(x : Double, df : Double) -> Double

The survival function of the chi-square distribution.

compare_double

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fn compare_double(a : Double, b : Double) -> Int

Compare two doubles, returning a negative / zero / positive integer.

cov

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fn cov(x : Array[Double], y : Array[Double]) -> Double

Sample covariance (ddof=1, matching numpy.cov).

digamma

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fn digamma(x : Double) -> Double

The digamma function, the derivative of the logarithm of the gamma function.

This is the port of scipy.special.digamma, which the entropy estimator of the Kozachenko-Leonenko of the gcm package uses. The port uses the recurrence ψ(x + 1) = ψ(x) + 1 / x to walk up to an argument of at least ten and the asymptotic expansion of the remainder, which is the same expansion scipy uses.

For an integer n the value is the harmonic number H(n - 1) without the Euler-Mascheroni constant, so the two agree to about 2e-15 at n = 10000.

erf

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fn erf(x : Double) -> Double

Error function.

erfc

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fn erfc(x : Double) -> Double

Complementary error function.

It is 1 - erf(x), the probability that a normal distributed variable with the mean zero and the variance one half is above x.

The port computes it from the regularised upper incomplete gamma function with the shape one half, because erfc(x) = Q(1/2, x^2). The series and the continued fraction of that function are the ones of the gamma distribution, so the whole range of the arguments is covered with the precision of SciPy.

exp

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fn exp(x : Double) -> Double

The exponential of a number.

f_cdf

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fn f_cdf(f : Double, df1 : Double, df2 : Double) -> Double

The cumulative distribution function of the F distribution.

f_ppf

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fn f_ppf(p : Double, df1 : Double, df2 : Double) -> Double

The quantile function of the F distribution.

f_sf

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fn f_sf(f : Double, df1 : Double, df2 : Double) -> Double

The survival function of the F distribution.

gammainc

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fn gammainc(a : Double, x : Double) -> Double

The regularised lower incomplete gamma function.

It is P(a, x), the probability that a gamma distributed variable with the shape a and the scale 1 is at most x.

gammaincc

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fn gammaincc(a : Double, x : Double) -> Double

The regularised upper incomplete gamma function.

It is Q(a, x), the probability that a gamma distributed variable with the shape a and the scale 1 is more than x. It is the complement of gammainc, and it is computed without the subtraction of the two, so it keeps its precision where the complement of gammainc would lose it.

glm_fit

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fn glm_fit(x : Matrix, y : Array[Double], family : GlmFamily, max_iter : Int, tol : Double) -> GlmFit

Fit a generalised linear model.

x is the design matrix, the intercept column included when one is wanted, and y the response vector.

glm_link_derivative

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fn glm_link_derivative(family : GlmFamily, mu : Array[Double]) -> Array[Double]

The derivative of the inverse link of a family, evaluated at the means of the response.

The derivative is what the delta method needs to turn the covariance of the coefficients into the variance of an estimate that is a function of them.

glm_predict

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fn glm_predict(fit : GlmFit, x : Matrix) -> Array[Double]

The predicted means of a generalised linear model.

is_nan

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fn is_nan(x : Double) -> Bool

Whether the value is "not a number".

jacobi_eigen

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fn jacobi_eigen(a : Matrix) -> (Array[Double], Matrix)

Symmetric eigen decomposition by the cyclic Jacobi method.

Returns the eigenvalues together with the eigenvectors stored as columns.

The iteration stops when the off-diagonal part of the matrix is negligible against the matrix itself: the sum of the squares of the off-diagonal elements has to be at most the square of the machine epsilon times the sum of the squares of the elements of the matrix. The criterion is relative on purpose. An absolute criterion leaves the off-diagonal elements of the matrix at a size of about 3e-8, which is enough for the eigenvalues of a matrix with a well separated spectrum, but not for the eigenvalues of a nearly degenerate one: those are then only accurate to about 1e-9.

kendall_tau

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fn kendall_tau(x : Array[Double], y : Array[Double]) -> Double

The Kendall rank correlation of two samples.

It is the tau-b variant, the one scipy.stats.kendalltau computes by default.

ln

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fn ln(x : Double) -> Double

The natural logarithm of a positive number.

ln_gamma

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fn ln_gamma(x : Double) -> Double

Natural logarithm of the gamma function (Lanczos approximation).

logistic_fit

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fn logistic_fit(x : Matrix, y : Array[Double], c : Double, max_iter : Int, tol : Double) -> LogisticFit

Fit a logistic regression with an L2 penalty.

The objective minimised is sum_i log_loss(y_i, p_i) + 1/(2C) * ||w||², which is the convention used by sklearn.linear_model.LogisticRegression with the default penalty="l2" and C=1.0.

logistic_predict

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fn logistic_predict(beta : Array[Double], x : Matrix) -> Array[Double]

Predicted probabilities of a logistic model.

lstsq

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fn lstsq(a : Matrix, b : Array[Double]) -> Array[Double]

Least squares solution of A x ≈ b (minimum norm when rank deficient).

mat_determinant

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fn mat_determinant(m : Matrix) -> Double

The determinant of a square matrix, by Gaussian elimination with partial pivoting.

The determinant of a matrix that is not square is zero. The elimination is the one of numpy.linalg.det, so the result is the same number.

mat_inverse

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fn mat_inverse(m : Matrix) -> Matrix?

Invert a square matrix with Gauss-Jordan elimination and partial pivoting.

Returns None when the matrix is singular.

mat_pinv

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fn mat_pinv(a : Matrix) -> Matrix

Moore-Penrose pseudo inverse of a matrix.

The pseudo inverse is obtained from the eigen decomposition of AᵀA, so rank deficient designs give the minimum norm least squares solution, the same convention statsmodels uses for OLS.

mean

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fn mean(values : Array[Double]) -> Double

Arithmetic mean of an array.

median

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fn median(values : Array[Double]) -> Double

Median of an array.

nan

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fn nan() -> Double

The "not a number" value, like numpy.nan.

The p-value merging of the gcm package drops the values that are not a number, so the value has to be reachable from there.

normal_cdf

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fn normal_cdf(z : Double) -> Double

Cumulative distribution function of the standard normal distribution.

normal_ppf

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fn normal_ppf(p : Double) -> Double

Inverse of the standard normal cumulative distribution function.

ols_fit

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fn ols_fit(x : Matrix, y : Array[Double]) -> OlsFit

Fit an ordinary least squares model.

x is the design matrix (already including the intercept column when one is wanted) and y the response vector.

pearson_corr

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fn pearson_corr(x : Array[Double], y : Array[Double]) -> Double

The Pearson correlation of two samples.

percentile

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fn percentile(values : Array[Double], q : Double) -> Double

Linear-interpolation percentile of an array, matching numpy.percentile.

q is expressed in the 0..100 range.

round_half_even

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fn round_half_even(x : Double) -> Double

Round half to even, matching numpy.round / pandas.Series.round(0).

sigmoid

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fn sigmoid(x : Double) -> Double

Logistic function.

spearman_corr

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fn spearman_corr(x : Array[Double], y : Array[Double]) -> Double

The Spearman rank correlation of two samples.

It is the Pearson correlation of the ranks, and the ranks of a tie get the mean rank, exactly like pandas.Series.rank.

std

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fn std(values : Array[Double]) -> Double

Population standard deviation (ddof=0).

std_sample

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fn std_sample(values : Array[Double]) -> Double

Sample standard deviation (ddof=1).

t_cdf

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fn t_cdf(t : Double, df : Double) -> Double

Cumulative distribution function of Student's t distribution.

t_ppf

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fn t_ppf(p : Double, df : Double) -> Double

Quantile of the Student's t distribution.

t_pvalue

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fn t_pvalue(t : Double, df : Double) -> Double

Two sided p-value of a t statistic.

var_pop

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fn var_pop(values : Array[Double]) -> Double

Population variance (ddof=0).

var_sample

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fn var_sample(values : Array[Double]) -> Double

Sample variance (ddof=1).

variance

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fn variance(values : Array[Double], ddof : Int) -> Double

Sample variance with the given delta degrees of freedom.

Source Files

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MoonBit port of DoWhy 0.14 (PyWhy). Causal graph construction and analysis, effect identification (backdoor / frontdoor / complete adjustment), estimation (linear regression, generalized linear model, propensity score weighting / matching / stratification, doubly robust, instrumental variable, two stage, regression discontinuity), refutation (bootstrap, placebo treatment, data subset, dummy outcome, unobserved common cause), intervention sampling (do samplers), temporal graphs, causal discovery (the PC algorithm with the Fisher-z test) and the portable core of the graphical causal models (the p-value merging, the bootstrap confidence intervals, the Kullback-Leibler divergences, the density estimators, the Shapley values, the independence tests, the prediction models, the causal mechanisms, the fitting of a causal model, the what-if queries (the interventional samples, the counterfactual samples and the average causal effect), the validation layer (the kernel based conditional independence test, the validation of a causal structure and the validation of an invertible model) and the falsification layer (the local Markov condition, the pairwise dependencies, the parental d-separations, the causal minimality and the permutation test of a graph) and the model evaluation layer (the normalised mean squared error, the continuous ranked probability score, the performance of the causal mechanisms, the test of the invertibility assumption and the report of the evaluation) and the distribution change layer (the test of the change of a mechanism, the attribution of the change of the distribution of a target node and the scores of the change of the distribution of every node). Pure MoonBit with zero external runtime dependencies.

causal-inferencedowhycausal-graphcausal-discoverybackdoorfrontdoorpropensity-scoretreatment-effectrefutationidentifiersestimatorsshapley-valuesindependence-teststructural-causal-modelcausal-mechanismwhat-ifcounterfactual

riantr

MIT

gitee.com/ren-yongxiang/moonbit_doWhy

Updated 2 hours ago

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#GlmFamily

#GlmFamily::binomial

#GlmFamily::gaussian

#GlmFamily::name

#GlmFamily::poisson

#GlmFit

#GlmFit::empty

#LogisticFit

#Matrix

#Matrix::col

#Matrix::copy

#Matrix::from_columns

#Matrix::from_flat

#Matrix::from_rows

#Matrix::get

#Matrix::identity

#Matrix::matvec

#Matrix::matvec_t

#Matrix::mul

#Matrix::mul_t

#Matrix::ncols

#Matrix::nrows

#Matrix::row

#Matrix::set

#Matrix::transpose

#Matrix::zeros

#OlsFit

#OlsFit::empty

#Random

#Random::new

#Random::next_double

#Random::next_int

#Random::next_normal

#Random::next_u64

#Random::sample_with_replacement

#Random::shuffle

#average_rank

#betainc

#chi2_cdf

#chi2_ppf

#chi2_sf

#compare_double

#cov

#digamma

#erf

#erfc

#exp

#f_cdf

#f_ppf

#f_sf

#gammainc

#gammaincc

#glm_fit

#glm_link_derivative

#glm_predict

#is_nan

#jacobi_eigen

#kendall_tau

#ln

#ln_gamma

#logistic_fit

#logistic_predict

#lstsq

#mat_determinant

#mat_inverse

#mat_pinv

#mean

#median

#nan

#normal_cdf

#normal_ppf

#ols_fit

#pearson_corr

#percentile

#round_half_even

#sigmoid

#spearman_corr

#std

#std_sample

#t_cdf

GlmFamily

GlmFamily::binomial

GlmFamily::gaussian

GlmFamily::name

GlmFamily::poisson

GlmFit

GlmFit::empty

LogisticFit

Matrix

Matrix::col

Matrix::copy

Matrix::from_columns

Matrix::from_flat

Matrix::from_rows

Matrix::get

Matrix::identity

Matrix::matvec

Matrix::matvec_t

Matrix::mul

Matrix::mul_t

Matrix::ncols

Matrix::nrows

Matrix::row

Matrix::set

Matrix::transpose

Matrix::zeros

OlsFit

OlsFit::empty

Random

Random::new

Random::next_double

Random::next_int

Random::next_normal

Random::next_u64

Random::sample_with_replacement

Random::shuffle

average_rank

betainc

chi2_cdf

chi2_ppf

chi2_sf

compare_double

cov

digamma

erf

erfc

exp

f_cdf

f_ppf

f_sf

gammainc

gammaincc

glm_fit

glm_link_derivative

glm_predict

is_nan

jacobi_eigen

kendall_tau

ln

ln_gamma

logistic_fit

logistic_predict

lstsq

mat_determinant

mat_inverse

mat_pinv

mean

median

nan

normal_cdf

normal_ppf

ols_fit

pearson_corr

percentile

round_half_even

sigmoid

spearman_corr

std

std_sample

t_cdf