EST_ols.cc

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/*                       Author :  Alan W Black (and lots of books)      */
/*                       Date   :  January 1998                          */
/*-----------------------------------------------------------------------*/
/* Ordinary Least Squares/Linear regression                              */
/*                                                                       */
/*=======================================================================*/
#include <cmath>
#include "EST_multistats.h"
#include "EST_simplestats.h"

using namespace std;

static void ols_load_selected_feats(const EST_FMatrix &X, 
                    const EST_IVector &included,
                    EST_FMatrix &Xl);
static int ols_stepwise_find_best(const EST_FMatrix &X,
                  const EST_FMatrix &Y,
                  EST_IVector &included,
                  EST_FMatrix &coeffs,
                  float &bscore,
                  int &best_feat,
                  const EST_FMatrix &Xtest,
                  const EST_FMatrix &Ytest,
                                  const EST_StrList &feat_names
                                  );

int ols(const EST_FMatrix &X,const EST_FMatrix &Y, EST_FMatrix &coeffs)
{
    // Ordinary least squares, X contains the samples with 1 (for intercept)
    // in column 0, Y contains the single values.
    EST_FMatrix Xplus;

    if (!pseudo_inverse(X,Xplus))
    return FALSE;

    multiply(Xplus,Y,coeffs);

    return TRUE;
}

int robust_ols(const EST_FMatrix &X,
           const EST_FMatrix &Y, 
           EST_FMatrix &coeffs)
{
    EST_IVector included;
    int i;

    included.resize(X.num_columns());
    for (i=0; i<included.length(); i++)
     included.a_no_check(i) = TRUE;

    return robust_ols(X,Y,included,coeffs);
}

int robust_ols(const EST_FMatrix &X,
           const EST_FMatrix &Y, 
           EST_IVector &included,
           EST_FMatrix &coeffs)
{
    // as with ols but if the pseudo inverse fails remove the offending
    // features and try again until it works, this can be costly but
    // its saves *you* from finding the singularity
    // This expands the output and puts weights of 0 for omitted features
    EST_FMatrix Xl;
    EST_FMatrix coeffsl;
    EST_FMatrix Xplus;
    int i,j,singularity=-1;

    if (X.num_rows() <= X.num_columns())
    {
    cerr << "OLS: less rows than columns, so cannot find solution."
        << endl;
    return FALSE;
    }
    if (X.num_columns() != included.length())
    {
    cerr << "OLS: `included' list wrong size: internal error."
        << endl;
    return FALSE;
    }

    while (TRUE)
    {
    ols_load_selected_feats(X,included,Xl);
    if (pseudo_inverse(Xl,Xplus,singularity))
    {
        multiply(Xplus,Y,coeffsl);
        break;
    }
    else
    {   // found a singularity so try again without that column
        // remap singularity position back to X
        int s;
        for (s=i=0; i<singularity; i++)
        {
        s++;
        while ((included(s) == FALSE) ||
                       (included(s) == OLS_IGNORE))
                       s++;
        }
        if (included(s) == FALSE)
        {   // oops
        cerr << "OLS: found singularity twice, shouldn't happen" 
            << endl;
        return FALSE;
        }
        else
        {
        cerr << "OLS: omitting singularity in column " << s << endl;
        included[s] = FALSE;
        }
    }
    }
     
    // Map coefficients back, making coefficient 0 for singular cols
    coeffs.resize(X.num_columns(),1);
    for (j=i=0; i<X.num_columns(); i++)
    if (included(i))
    {
        coeffs.a_no_check(i,0) = coeffsl(j,0);
        j++;
    }
    else
        coeffs.a_no_check(i,0) = 0.0;


    return TRUE;

}

static void ols_load_selected_feats(const EST_FMatrix &X, 
                    const EST_IVector &included,
                    EST_FMatrix &Xl)
{
    int i,j,k,width;

    for (width=i=0; i<included.length(); i++)
    if (included(i) == TRUE)
        width++;

    Xl.resize(X.num_rows(),width);

    for (i=0; i<X.num_rows(); i++)
    for (k=j=0; j < X.num_columns(); j++)
        if (included(j) == TRUE)
        {
        Xl.a_no_check(i,k) = X.a_no_check(i,j);
        k++;
        }
     
}

int ols_apply(const EST_FMatrix &samples,
          const EST_FMatrix &coeffs,
          EST_FMatrix &res)
{
    // Apply coefficients to samples for res.

    if (samples.num_columns() != coeffs.num_rows())
    return FALSE;

    multiply(samples,coeffs,res);

    return TRUE;
}

int stepwise_ols(const EST_FMatrix &X,
         const EST_FMatrix &Y,
         const EST_StrList &feat_names,
         float limit,
         EST_FMatrix &coeffs,
         const EST_FMatrix &Xtest,
         const EST_FMatrix &Ytest,
                 EST_IVector &included)
{
    // Find the features that contribute to the correlation using a
    // a greedy algorithm

    EST_FMatrix coeffsl;
    float best_score=0.0,bscore;
    int i,best_feat;
    int nf=1;  // for nice printing of progress

    for (i=1; i < X.num_columns(); i++)
    {
    if (!ols_stepwise_find_best(X,Y,included,coeffsl,
                    bscore,best_feat,Xtest,Ytest,
                                    feat_names))
    {
        cerr << "OLS: stepwise failed" << endl;
        return FALSE;
    }
    if ((bscore - (bscore * (limit/100))) <= best_score)
        break;
    else
    {
        best_score = bscore;
        coeffs = coeffsl;
        included[best_feat] = TRUE;
        printf("FEATURE %d %s: %2.4f\n",
           nf,
           (const char *)feat_names.nth(best_feat),
           best_score);
        fflush(stdout);
        nf++;
    }
    }

    return TRUE;
}

static int ols_stepwise_find_best(const EST_FMatrix &X,
                  const EST_FMatrix &Y,
                  EST_IVector &included,
                  EST_FMatrix &coeffs,
                  float &bscore,
                  int &best_feat,
                  const EST_FMatrix &Xtest,
                  const EST_FMatrix &Ytest,
                                  const EST_StrList &feat_names
                                  )
{
    EST_FMatrix coeffsl;
    bscore = 0;
    best_feat = -1;
    int i;

    for (i=0; i < included.length(); i++)
    {
    if (included.a_no_check(i) == FALSE)
    {
        float cor, rmse;
        EST_FMatrix pred;
        included.a_no_check(i) = TRUE;
        if (!robust_ols(X,Y,included,coeffsl)) {
            included.a_no_check(i) = FALSE; /* restore previous status */
            return FALSE;  // failed for some reason
        }
        ols_apply(Xtest,coeffsl,pred);
        ols_test(Ytest,pred,cor,rmse);
            printf("tested %d %s %f best %f\n",
                   i,(const char *)feat_names.nth(i),cor,bscore);
        if (fabs(cor) > bscore)
        {
        bscore = fabs(cor);
        coeffs = coeffsl;
        best_feat = i;
        }
        included.a_no_check(i) = FALSE;
    }
    }

    return TRUE;
}

int ols_test(const EST_FMatrix &real,
         const EST_FMatrix &predicted,
         float &correlation,
         float &rmse)
{
    // Others probably want this function too
    // return correlation and RMSE for col 0 in real and predicted
    int i;
    float p,r;
    EST_SuffStats x,y,xx,yy,xy,se,e;
    double error;
    double v1,v2,v3;

    if (real.num_rows() != predicted.num_rows())
    {
        correlation = 0;
        return FALSE;  // can't do this
    }

    for (i=0; i < real.num_rows(); i++)
    {
    r = real(i,0);
    p = predicted(i,0);
    x += p;
    y += r;
    error = p-r;
    se += error*error;
    e += fabs(error);
    xx += p*p;
    yy += r*r;
    xy += p*r;
    }

    rmse = sqrt(se.mean());

    v1 = xx.mean()-(x.mean()*x.mean());
    v2 = yy.mean()-(y.mean()*y.mean());

    v3 = v1*v2;

    if (v3 <= 0)
    {   // happens when there's very little variation in x
    correlation = 0;
    rmse = se.mean();
    return FALSE;
    }
    // Pearson's product moment correlation coefficient
    correlation = (xy.mean() - (x.mean()*y.mean()))/ sqrt(v3);

    // I hate to have to do this but it is necessary.
    // When the the variation of X is very small v1*v2 approaches
    // 0 (the negative and equals case is caught above) but that
    // may not be enough when v1 or v2 are very small but positive.
    // So I catch it here.  If I knew more math I'd be able to describe
    // this better but the code would remain the same.
    if ((correlation <= 1.0) && (correlation >= -1.0))
    return TRUE;
    else
    {
    correlation = 0;
    return FALSE;
    }
}