public static double NormalCdf(double x, double mean, double variance)
{
double centered = x - mean;
double ztrans = centered / (Math.Sqrt(variance) * Math.Sqrt(2));
return(0.5 * (1 + ProbabilityFunctions.Erf(ztrans)));
}
public static bool TryGetBiasStatistics(LinearModelStatistics stats, Single bias, out Single stdError, out Single zScore, out Single pValue)
{
if (!stats._coeffStdError.HasValue)
{
stdError = 0;
zScore = 0;
pValue = 0;
return(false);
}
const Double sqrt2 = 1.41421356237; // Math.Sqrt(2);
stdError = stats._coeffStdError.Value.Values[0];
Contracts.Assert(stdError == stats._coeffStdError.Value.GetItemOrDefault(0));
zScore = bias / stdError;
pValue = 1 - (Single)ProbabilityFunctions.Erf(Math.Abs(zScore / sqrt2));
return(true);
}
private IEnumerable <CoefficientStatistics> GetUnorderedCoefficientStatistics(LinearBinaryPredictor parent, RoleMappedSchema schema)
{
Contracts.AssertValue(_env);
_env.CheckValue(parent, nameof(parent));
if (!_coeffStdError.HasValue)
{
yield break;
}
var weights = parent.Weights2 as IReadOnlyList <Single>;
_env.Assert(_paramCount == 1 || weights != null);
_env.Assert(_coeffStdError.Value.Length == weights.Count + 1);
var names = default(VBuffer <ReadOnlyMemory <char> >);
MetadataUtils.GetSlotNames(schema, RoleMappedSchema.ColumnRole.Feature, weights.Count, ref names);
Single[] stdErrorValues = _coeffStdError.Value.Values;
const Double sqrt2 = 1.41421356237; // Math.Sqrt(2);
bool denseStdError = _coeffStdError.Value.IsDense;
int[] stdErrorIndices = _coeffStdError.Value.Indices;
Single[] zScores = new Single[_paramCount - 1];
for (int i = 1; i < _paramCount; i++)
{
int wi = denseStdError ? i - 1 : stdErrorIndices[i] - 1;
_env.Assert(0 <= wi && wi < weights.Count);
var name = names.GetItemOrDefault(wi).ToString();
if (string.IsNullOrEmpty(name))
{
name = $"f{wi}";
}
var weight = weights[wi];
var stdError = stdErrorValues[i];
var zScore = zScores[i - 1] = weight / stdError;
var pValue = 1 - (Single)ProbabilityFunctions.Erf(Math.Abs(zScore / sqrt2));
yield return(new CoefficientStatistics(name, weight, stdError, zScore, pValue));
}
}
private Double ComputeKernelPValue(Double rawScore)
{
int i;
int n = RawScoreBuffer.Count;
if (n == 0)
{
return(0.5);
}
Double pValue = 0;
Double bandWidth = Math.Sqrt(2) * ((n == 1) ? 1 : Math.Sqrt(_sumSquaredDist) / n);
bandWidth = Math.Max(bandWidth, 1e-6);
Double diff;
for (i = 0; i < n; ++i)
{
diff = rawScore - RawScoreBuffer[i];
pValue -= ProbabilityFunctions.Erf(diff / bandWidth);
_sumSquaredDist += diff * diff;
}
pValue = 0.5 + pValue / (2 * n);
if (RawScoreBuffer.IsFull)
{
for (i = 1; i < n; ++i)
{
diff = RawScoreBuffer[0] - RawScoreBuffer[i];
_sumSquaredDist -= diff * diff;
}
diff = RawScoreBuffer[0] - rawScore;
_sumSquaredDist -= diff * diff;
}
return(pValue);
}
public static double StdNormalCdf(double x)
{
return(0.5 * (1 + ProbabilityFunctions.Erf(x * 1 / Math.Sqrt(2))));
}
private static void GetUnorderedCoefficientStatistics(LinearModelStatistics stats, ref VBuffer <Single> weights, ref VBuffer <ReadOnlyMemory <char> > names,
ref VBuffer <Single> estimate, ref VBuffer <Single> stdErr, ref VBuffer <Single> zScore, ref VBuffer <Single> pValue, out ValueGetter <VBuffer <ReadOnlyMemory <char> > > getSlotNames)
{
if (!stats._coeffStdError.HasValue)
{
getSlotNames = null;
return;
}
Contracts.Assert(stats._coeffStdError.Value.Length == weights.Length + 1);
var estimateValues = estimate.Values;
if (Utils.Size(estimateValues) < stats.ParametersCount - 1)
{
estimateValues = new Single[stats.ParametersCount - 1];
}
var stdErrorValues = stdErr.Values;
if (Utils.Size(stdErrorValues) < stats.ParametersCount - 1)
{
stdErrorValues = new Single[stats.ParametersCount - 1];
}
var zScoreValues = zScore.Values;
if (Utils.Size(zScoreValues) < stats.ParametersCount - 1)
{
zScoreValues = new Single[stats.ParametersCount - 1];
}
var pValueValues = pValue.Values;
if (Utils.Size(pValueValues) < stats.ParametersCount - 1)
{
pValueValues = new Single[stats.ParametersCount - 1];
}
const Double sqrt2 = 1.41421356237; // Math.Sqrt(2);
bool denseStdError = stats._coeffStdError.Value.IsDense;
int[] stdErrorIndices = stats._coeffStdError.Value.Indices;
for (int i = 1; i < stats.ParametersCount; i++)
{
int wi = denseStdError ? i - 1 : stdErrorIndices[i] - 1;
Contracts.Assert(0 <= wi && wi < weights.Length);
var weight = estimateValues[i - 1] = weights.GetItemOrDefault(wi);
var stdError = stdErrorValues[wi] = stats._coeffStdError.Value.Values[i];
zScoreValues[i - 1] = weight / stdError;
pValueValues[i - 1] = 1 - (Single)ProbabilityFunctions.Erf(Math.Abs(zScoreValues[i - 1] / sqrt2));
}
estimate = new VBuffer <Single>(stats.ParametersCount - 1, estimateValues, estimate.Indices);
stdErr = new VBuffer <Single>(stats.ParametersCount - 1, stdErrorValues, stdErr.Indices);
zScore = new VBuffer <Single>(stats.ParametersCount - 1, zScoreValues, zScore.Indices);
pValue = new VBuffer <Single>(stats.ParametersCount - 1, pValueValues, pValue.Indices);
var slotNames = names;
getSlotNames =
(ref VBuffer <ReadOnlyMemory <char> > dst) =>
{
var values = dst.Values;
if (Utils.Size(values) < stats.ParametersCount - 1)
{
values = new ReadOnlyMemory <char> [stats.ParametersCount - 1];
}
for (int i = 1; i < stats.ParametersCount; i++)
{
int wi = denseStdError ? i - 1 : stdErrorIndices[i] - 1;
values[i - 1] = slotNames.GetItemOrDefault(wi);
}
dst = new VBuffer <ReadOnlyMemory <char> >(stats.ParametersCount - 1, values, dst.Indices);
};
}
public static double erf(double x) => ProbabilityFunctions.Erf(x);