glm
Version:
Generalized Linear Models
964 lines (863 loc) • 29.9 kB
JavaScript
(function(exports){
exports.GLM = function (family, regularization) {
/* Set defaults */
// default family is Gaussian (linear model)
if (!family) { family = exports.GLM.families.Gaussian(); }
// default to no regularization (none supported yet)
if (!regularization) { regularization = 'none'; }
// the returned model
var model = {};
model.family = family;
model.weights = null;
function constantize (exogenous) {
if (!exports.GLM.utils.isArray(exogenous[0])) {
exogenous = exports.GLM.utils.transpose(exports.GLM.utils.atleast_2d(exogenous));
}
return exports.GLM.utils.add_constant(exogenous);
}
model.fit = function (endogenous, exogenous) {
exogenous = constantize(exogenous);
model.weights = exports.GLM.optimization.IRLS(endogenous, exogenous, model.family);
return this;
};
model.predict = function (exogenous) {
exogenous = constantize(exogenous)
var linear = exports.GLM.utils.dot(exogenous, model.weights);
return model.family.fitted(linear);
};
return model;
}
/******************************************************************\
For an m-by-n matrix A with m >= n, the Thin Singular Value Decomposition
(See: http://en.wikipedia.org/wiki/Singular_value_decomposition#Thin_SVD )
returns:
- an m-by-n matrix U with orthogonal columns,
- an n-by-n diagonal matrix S,
- and an n-by-n orthogonal matrix V
such that A = U*S*V'. (here V' indicates the transposed of V)
The function thinsvd(A), for m >=n, returns an array containing:
- an m x n bidimensional array U with orthogonal columns
- an m-sized unidimensional array containing the n singular values, sorted in descending order
- an n x n bidimensional orthogonal array containing V (NOTE: _not_ V' as NumPy's linalg.svd(A,full_matrices=0) does!!)
If m < n, it returns an array containing:
- an m x m bidimensional array containing U
- an m-sized unidimensional array containing the n singular values, sorted in descending order
- an m x n bidimensional array V with orthogonal columns
The Singular Values s[] allow to compute the following values of the input argument:
- Two norm l2n = s[0]
- Condition number cn = l2n / s[Math.min(m,n)-1]
- Rank r = number of singular values larger than cn * eps,
(eps being 2.22E-16 i.e. Math.pow(2.0,-52.0)
With square random matrices, complexity grows as O(n^3)
Decomposing a 100x100 matrix typically takes, with a
single-core 1.7GHz Pentium M:
- Chrome 3.0.195.27: 880 ms
- Firefox 3.5.4: 950 ms
- Safari 4.0.3: 1,360 ms
- MSIE 8.0: 9,554 ms (and three "slow script" warnings)
\******************************************************************/
var hypot = function(a, b) {
var at = Math.abs(a);
var bt = Math.abs(b);
var q;
if( at > bt ) {
q = bt / at;
return at * Math.sqrt( 1.0 + q*q );
} else {
if ( bt > 0.0 ){
q = at / bt;
return bt * Math.sqrt( 1.0 + q*q );
} else {
return 0.0;
}
}
};
exports.GLM.thinsvd = function (A) {
// Derived from JAMA public domain code: http://math.nist.gov/javanumerics/jama/
var i, j, k, t, f, g, cs, sn;
var lowrise = (A.length < A[0].length); // if true, then rows < columns. in that case, transpose A and exchange U and V on return
// make a copy, so the original matrix will be preserved
var AT = [];
if(lowrise) {
for(i=0; i<A[0].length; i++) {
AT[i] = [];
for(j=0; j<A.length; j++) {
AT[i][j] = A[j][i]; // swap rows with columns
}
}
} else {
for(i=0; i<A.length; i++) {
AT[i] = [];
for(j=0; j<A[0].length; j++) {
AT[i][j] = A[i][j]; // swap rows with columns
}
}
}
A = AT;
var m = A.length;
var n = A[0].length;
var nu = Math.min(m,n);
var s = [];
var U = [];
for(i=0; i<m; i++) {
U[i] = [];
for(j=0; j<n; j++) {
U[i][j] = 0.;
}
}
var V = [];
for(i=0; i<n; i++) {
V[i] = [];
}
var e = [];
var work = [];
var wantu = true;
var wantv = true;
// Reduce A to bidiagonal form, storing the diagonal elements
// in s and the super-diagonal elements in e.
var nct = Math.min(m-1,n);
var nrt = Math.max(0,Math.min(n-2,m));
for (k = 0; k < Math.max(nct,nrt); k++) {
if (k < nct) {
// Compute the transformation for the k-th column and
// place the k-th diagonal in s[k].
// Compute 2-norm of k-th column without under/overflow.
s[k] = 0;
for (i = k; i < m; i++) {
s[k] = hypot(s[k],A[i][k]);
}
if (s[k] !== 0.0) {
if (A[k][k] < 0.0) {
s[k] = -s[k];
}
for (i = k; i < m; i++) {
A[i][k] /= s[k];
}
A[k][k] += 1.0;
}
s[k] = -s[k];
}
for (j = k+1; j < n; j++) {
if ((k < nct) && (s[k] !== 0.0)) {
// Apply the transformation.
t = 0;
for (i = k; i < m; i++) {
t += A[i][k]*A[i][j];
}
t = -t/A[k][k];
for (i = k; i < m; i++) {
A[i][j] += t*A[i][k];
}
}
// Place the k-th row of A into e for the
// subsequent calculation of the row transformation.
e[j] = A[k][j];
}
if (wantu && (k < nct)) {
// Place the transformation in U for subsequent back
// multiplication.
for (i = k; i < m; i++) {
U[i][k] = A[i][k];
}
}
if (k < nrt) {
// Compute the k-th row transformation and place the
// k-th super-diagonal in e[k].
// Compute 2-norm without under/overflow.
e[k] = 0;
for (i = k+1; i < n; i++) {
e[k] = hypot(e[k],e[i]);
}
if (e[k] !== 0.0) {
if (e[k+1] < 0.0) {
e[k] = -e[k];
}
for (i = k+1; i < n; i++) {
e[i] /= e[k];
}
e[k+1] += 1.0;
}
e[k] = -e[k];
if ((k+1 < m) && (e[k] !== 0.0)) {
// Apply the transformation.
for (i = k+1; i < m; i++) {
work[i] = 0.0;
}
for (j = k+1; j < n; j++) {
for (i = k+1; i < m; i++) {
work[i] += e[j]*A[i][j];
}
}
for (j = k+1; j < n; j++) {
t = -e[j]/e[k+1];
for (i = k+1; i < m; i++) {
A[i][j] += t*work[i];
}
}
}
if (wantv) {
// Place the transformation in V for subsequent
// back multiplication.
for (i = k+1; i < n; i++) {
V[i][k] = e[i];
}
}
}
}
// Set up the final bidiagonal matrix or order p.
var p = Math.min(n,m+1);
if (nct < n) {
s[nct] = A[nct][nct];
}
if (m < p) {
s[p-1] = 0.0;
}
if (nrt+1 < p) {
e[nrt] = A[nrt][p-1];
}
e[p-1] = 0.0;
// If required, generate U.
if (wantu) {
for (j = nct; j < nu; j++) {
for (i = 0; i < m; i++) {
U[i][j] = 0.0;
}
U[j][j] = 1.0;
}
for (k = nct-1; k >= 0; k--) {
if (s[k] !== 0.0) {
for (j = k+1; j < nu; j++) {
t = 0;
for (i = k; i < m; i++) {
t += U[i][k]*U[i][j];
}
t = -t/U[k][k];
for (i = k; i < m; i++) {
U[i][j] += t*U[i][k];
}
}
for (i = k; i < m; i++ ) {
U[i][k] = -U[i][k];
}
U[k][k] = 1.0 + U[k][k];
for (i = 0; i < k-1; i++) {
U[i][k] = 0.0;
}
} else {
for (i = 0; i < m; i++) {
U[i][k] = 0.0;
}
U[k][k] = 1.0;
}
}
}
// If required, generate V.
if (wantv) {
for (k = n-1; k >= 0; k--) {
if ((k < nrt) && (e[k] !== 0.0)) {
for (j = k+1; j < nu; j++) {
t = 0;
for (i = k+1; i < n; i++) {
t += V[i][k]*V[i][j];
}
t = -t/V[k+1][k];
for (i = k+1; i < n; i++) {
V[i][j] += t*V[i][k];
}
}
}
for (i = 0; i < n; i++) {
V[i][k] = 0.0;
}
V[k][k] = 1.0;
}
}
// Main iteration loop for the singular values.
var pp = p-1;
var iter = 0;
var totiter = 0;
var eps = 2.2205E-16; // Math.pow(2.0,-52.0);
var tiny = 1.6034E-291; // Math.pow(2.0,-966.0);
while (p > 0) {
var kase;
// Here is where a test for too many iterations would go.
// This section of the program inspects for
// negligible elements in the s and e arrays. On
// completion the variables kase and k are set as follows.
// kase = 1 if s(p) and e[k-1] are negligible and k<p
// kase = 2 if s(k) is negligible and k<p
// kase = 3 if e[k-1] is negligible, k<p, and
// s(k), ..., s(p) are not negligible (qr step).
// kase = 4 if e(p-1) is negligible (convergence).
for (k = p-2; k >= -1; k--) {
if (k == -1) {
break;
}
if (Math.abs(e[k]) <= tiny + eps*(Math.abs(s[k]) + Math.abs(s[k+1]))) {
e[k] = 0.0;
break;
}
}
if (k == p-2) {
kase = 4;
} else {
var ks;
for (ks = p-1; ks >= k; ks--) {
if (ks == k) {
break;
}
t = (ks != p ? Math.abs(e[ks]) : 0.0) + (ks != k+1 ? Math.abs(e[ks-1]) : 0.0);
if (Math.abs(s[ks]) <= tiny + eps*t) {
s[ks] = 0.0;
break;
}
}
if (ks == k) {
kase = 3;
} else if (ks == p-1) {
kase = 1;
} else {
kase = 2;
k = ks;
}
}
k++;
// Perform the task indicated by kase.
if(kase == 1) {
// Deflate negligible s(p).
f = e[p-2];
e[p-2] = 0.0;
for (j = p-2; j >= k; j--) {
t = hypot(s[j],f);
cs = s[j]/t;
sn = f/t;
s[j] = t;
if (j != k) {
f = -sn*e[j-1];
e[j-1] = cs*e[j-1];
}
if (wantv) {
for (i = 0; i < n; i++) {
t = cs*V[i][j] + sn*V[i][p-1];
V[i][p-1] = -sn*V[i][j] + cs*V[i][p-1];
V[i][j] = t;
}
}
}
} else if (kase == 2) {
f = e[k-1];
e[k-1] = 0.0;
for (j = k; j < p; j++) {
t = hypot(s[j],f);
cs = s[j]/t;
sn = f/t;
s[j] = t;
f = -sn*e[j];
e[j] = cs*e[j];
if (wantu) {
for (i = 0; i < m; i++) {
t = cs*U[i][j] + sn*U[i][k-1];
U[i][k-1] = -sn*U[i][j] + cs*U[i][k-1];
U[i][j] = t;
}
}
}
} else if (kase == 3) {
// Calculate the shift.
var scale = Math.max(Math.max(Math.max(Math.max(
Math.abs(s[p-1]),Math.abs(s[p-2])),Math.abs(e[p-2])),
Math.abs(s[k])),Math.abs(e[k]));
var sp = s[p-1]/scale;
var spm1 = s[p-2]/scale;
var epm1 = e[p-2]/scale;
var sk = s[k]/scale;
var ek = e[k]/scale;
var b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)/2.0;
var c = (sp*epm1)*(sp*epm1);
var shift = 0.0;
if ((b !== 0.0) || (c !== 0.0)) {
shift = Math.sqrt(b*b + c);
if (b < 0.0) {
shift = -shift;
}
shift = c/(b + shift);
}
f = (sk + sp)*(sk - sp) + shift;
g = sk*ek;
// Chase zeros.
for (j = k; j < p-1; j++) {
t = hypot(f,g);
cs = f/t;
sn = g/t;
if (j != k) {
e[j-1] = t;
}
f = cs*s[j] + sn*e[j];
e[j] = cs*e[j] - sn*s[j];
g = sn*s[j+1];
s[j+1] = cs*s[j+1];
if (wantv) {
for (i = 0; i < n; i++) {
t = cs*V[i][j] + sn*V[i][j+1];
V[i][j+1] = -sn*V[i][j] + cs*V[i][j+1];
V[i][j] = t;
}
}
t = hypot(f,g);
cs = f/t;
sn = g/t;
s[j] = t;
f = cs*e[j] + sn*s[j+1];
s[j+1] = -sn*e[j] + cs*s[j+1];
g = sn*e[j+1];
e[j+1] = cs*e[j+1];
if (wantu && (j < m-1)) {
for (i = 0; i < m; i++) {
t = cs*U[i][j] + sn*U[i][j+1];
U[i][j+1] = -sn*U[i][j] + cs*U[i][j+1];
U[i][j] = t;
}
}
}
e[p-2] = f;
iter = iter + 1;
} else if(kase == 4) {
// Convergence.
// Make the singular values positive.
if (s[k] <= 0.0) {
s[k] = (s[k] < 0.0 ? -s[k] : 0.0);
if (wantv) {
for (i = 0; i <= pp; i++) {
V[i][k] = -V[i][k];
}
}
}
// Order the singular values.
while (k < pp) {
if (s[k] >= s[k+1]) {
break;
}
t = s[k];
s[k] = s[k+1];
s[k+1] = t;
if (wantv && (k < n-1)) {
for (i = 0; i < n; i++) {
t = V[i][k+1]; V[i][k+1] = V[i][k]; V[i][k] = t;
}
}
if (wantu && (k < m-1)) {
for (i = 0; i < m; i++) {
t = U[i][k+1]; U[i][k+1] = U[i][k]; U[i][k] = t;
}
}
k++;
}
totiter += iter;
iter = 0;
p--;
}
}
if(lowrise) {
return [V,s,U,totiter];
} else {
return [U,s,V,totiter];
}
/*
Two norm: s[0]
Two norm condition number: s[0]/s[Math.min(m,n)-1]
Rank:
function rank (s) {
var eps = 2.22E-16; // Math.pow(2.0,-52.0);
tol = Math.max(m,n)*s[0]*eps;
var r = 0;
for (i = 0; i < s.length; i++) {
if (s[i] > tol) {
r++;
}
}
return r;
}
*/
}
exports.GLM.version = "1.0.0";
exports.GLM.testing = exports.GLM.testing || {};
exports.GLM.testing.arrayEqual = function (lhs, rhs) {
if (lhs.length != rhs.length) { return false;}
for (var i = 0; i < lhs.length; i++) {
if (lhs[i] != rhs[i]) {
return false;
}
}
return true;
};
exports.GLM.testing.fuzzyArrayEqual = function (lhs, rhs, tolerance) {
if (!tolerance) { tolerance = 1e-4; }
if (!exports.GLM.testing.arrayEqual(exports.GLM.utils.shape(lhs), exports.GLM.utils.shape(rhs))) { return false; }
if (exports.GLM.utils.isArray(lhs[0])) {
for (var i = 0; i < lhs.length; i++) {
if (!exports.GLM.testing.fuzzyArrayEqual(lhs[i], rhs[i], tolerance)) {
return false;
}
}
} else {
for (var i = 0; i < lhs.length; i++) {
if (Math.abs(lhs[i] - rhs[i]) > tolerance) {
return false;
}
}
}
return true;
};
exports.GLM.utils = exports.GLM.utils || {};
exports.GLM.utils.mean = function (vector) {
var sum = 0.0;
for (var i = 0; i < vector.length; i++) { sum += vector[i]; }
return sum / vector.length;
};
exports.GLM.utils.checkConvergence = function (newDev, oldDev, iterations, maxIterations) {
var tol = 1e-8;
return (oldDev != null && (Math.abs(newDev - oldDev) < tol)) || (iterations > maxIterations);
};
exports.GLM.utils.softThreshold = function (z, gamma) {
var z_abs = Math.abs(z);
if (gamma < z_abs) {
if (z > 0) {
return z - gamma;
} else {
return z + gamma;
}
} else {
return 0;
}
};
exports.GLM.utils.makeArray = function (n_zeros, initialValue) {
var vector = [];
for (var i = 0; i < n_zeros; i++) { vector.push(exports.GLM.utils.clone(initialValue)); }
return vector;
};
exports.GLM.utils.zeros = function (n_zeros) {
var currentFold;
if (exports.GLM.utils.isArray(n_zeros)) {
currentFold = exports.GLM.utils.makeArray(n_zeros[0], 0);
for (var i = 1; i < n_zeros.length; i++) {
currentFold = exports.GLM.utils.makeArray(n_zeros[i], currentFold);
}
} else {
currentFold = exports.GLM.utils.makeArray(n_zeros, 0);
}
return currentFold;
};
exports.GLM.utils.map = function (ary, fn) {
var out = [];
for (var i = 0; i < ary.length; i++) {
out.push(fn(ary[i], i));
}
return out;
};
exports.GLM.utils.isArray = function (potentialArray) {
return potentialArray.constructor == Array;
};
exports.GLM.utils.atleast_2d = function (A) {
// will make sure JS array is at least 2 dimensional
// assumption is that 1-d vectors are column vectors
if (exports.GLM.utils.isArray(A[0])) {
return A;
} else {
return [A];
}
};
exports.GLM.utils.add_constant = function (ary) {
exports.GLM.utils.map(ary, function (x) { x.push(1);});
return ary;
};
exports.GLM.utils.dot = function (a, b) {
var r, aIsM = exports.GLM.utils.isArray(a[0]), bIsM = exports.GLM.utils.isArray(b[0]), n_rows = a.length, n_columns = b[0].length;
if (aIsM & bIsM) { // both matrices
r = exports.GLM.utils.zeros([n_columns, n_rows]);
for (var i = 0; i < n_rows; i++) {
for (var j = 0; j < n_columns; j++) {
for (var k = 0; k < b.length; k++) {
r[i][j] += a[i][k] * b[k][j];
}
}
}
return r;
} else if (aIsM) {
return exports.GLM.utils.transpose(exports.GLM.utils.dot(a, exports.GLM.utils.transpose([b])))[0];
} else if (bIsM) {
return exports.GLM.utils.dot([a], b);
} else {
r = 0.0;
for (var i = 0; i < a.length; i++) {
r += a[i] * b[i];
}
return r;
}
};
exports.GLM.utils.shape = function (A) {
if (exports.GLM.utils.isArray(A[0])) {
return [A.length, A[0].length];
} else {
return [A.length];
}
};
exports.GLM.utils.transpose = function (A) {
var r = [];
A = exports.GLM.utils.atleast_2d(A);
for (var i = 0; i < A[0].length; i++) {
r[i] = exports.GLM.utils.zeros(A.length);
}
for (var i = 0; i < A.length; i++) {
for (var j = 0; j < A[0].length; j++) {
r[j][i] = A[i][j];
}
}
return r;
};
exports.GLM.utils.identity = function (size) {
var r = exports.GLM.utils.makeArray(size, exports.GLM.utils.makeArray(size, 0));
for (var i = 0; i < size; i++) { r[i][i] = 1; }
return r;
};
exports.GLM.utils.clone = function (obj) {
if (null == obj || "object" != typeof obj) return obj;
var copy = obj.constructor();
for (var attr in obj) {
if (obj.hasOwnProperty(attr)) {
copy[attr] = obj[attr];
}
}
return copy;
};
exports.GLM.utils.mul = function (A, B) {
return exports.GLM.utils.map(A, function (a, i) { return a * B[i]; });
};
exports.GLM.utils.inverse = function (matrix) {
// taken from wikipedia
var dimension = matrix.length, inverse = exports.GLM.utils.zeros([dimension, dimension]);
for (var i = 0; i < dimension; i++) {
for (var j = 0; j < dimension; j++) {
inverse[i][j] = 0;
}
}
for (var i = 0; i < dimension; i++) {
inverse[i][i] = 1;
}
for (var k = 0; k < dimension; k++) {
for (var i = k; i < dimension; i++) {
var val = matrix[i][k];
for (var j = k; j < dimension; j++) {
matrix[i][j] /= val;
}
for (var j = 0; j < dimension; j++) {
inverse[i][j] /= val;
}
}
for (var i = k + 1; i < dimension; i++) {
for (var j = k; j < dimension; j++) {
matrix[i][j] -= matrix[k][j];
}
for (var j = 0; j < dimension; j++) {
inverse[i][j] -= inverse[k][j];
}
}
}
for (var i = dimension - 2; i >= 0; i--) {
for (var j = dimension - 1; j > i; j--) {
for (var k = 0; k < dimension; k++) {
inverse[i][k] -= matrix[i][j] * inverse[j][k];
}
for (var k = 0; k < dimension; k++) {
matrix[i][k] -= matrix[i][j] * matrix[j][k];
}
}
}
return inverse;
};
exports.GLM.utils.linspace = function (lower, upper, number_of_steps) {
var linear_array = [], step_size = (upper + 0.0 - lower) / number_of_steps;
for (var i = 0; i < number_of_steps; i++) {
linear_array.push(lower + i * step_size);
}
return linear_array;
}
exports.GLM.families = exports.GLM.families || {};
exports.GLM.families.Binomial = function (link) {
// default to logit
if (!link) { link = exports.GLM.links.Logit(); }
model = {};
model.initialMu = function (y) {
var init = [];
for (var i = 0; i < y.length; i++) { init.push((y[i] + 0.5) / 2); }
return init;
};
model.deviance = function(endogenous, mu) {
// formula for binomial deviance
// 2 * sum{i \in y,mu}(log(Y/mu) + (n-Y)*log((n-Y)/(n-mu)))
var dev = 0.0;
for (var i = 0; i < mu.length; i++) {
var one = endogenous[i] == 1 ? 1 : 0;
dev += one * Math.log(mu[i] + 1e-200) + (1 - one) * Math.log(1 - mu[i] + 1e-200);
}
return 2 * dev;
};
// assign input link function
model.link = link;
model.predict = function (mu) {
return model.link(mu);
};
model.weights = function (mu) {
function fix(z) { if (z < 1e-10) { return 1e-10; } else { if (z > (1 - 1e-10)) { return 1 - 1e-10; } else { return z; } } }
var variance = exports.GLM.utils.map(mu, function(m) { return fix(m) * (1 - fix(m)) ;} );
return exports.GLM.utils.map(model.link.derivative(mu), function (m, i) { return 1.0 / (Math.pow(m, 2) * variance[i] ); });
};
model.fitted = function (eta) {
return model.link.inverse(eta);
};
return model;
};
exports.GLM.families.Gaussian = function (link) {
// default to identity link function
if (!link) { link = exports.GLM.links.Identity(); }
var model = {};
model.deviance = function (endogenous, mu) {
var dev = 0.0;
for (var i = 0; i < endogenous.length; i++) {
dev += Math.pow(endogenous[i] - mu[i], 2);
}
return dev;
};
model.initialMu = function (y) {
var y_mean = exports.GLM.utils.mean(y), mu = [];
for (var i = 0; i < y.length; i++) { mu.push((y[i] + y_mean) / 2.0); }
return mu;
};
model.link = link;
model.predict = function (mu) {
return model.link(mu);
};
model.weights = function (mu) {
// TODO write test & cleanup
var variance = exports.GLM.utils.makeArray(mu.length, 1);
return exports.GLM.utils.map(model.link.derivative(mu), function (m, i) { return 1.0 / (Math.pow(m, 2) / variance[i] ); });
};
model.fitted = function (eta) {
return model.link.inverse(eta);
};
return model;
};
exports.GLM.links = exports.GLM.links || {};
var linkBuilder = function (func, inv, deriv) {
var f = function (P) { return exports.GLM.utils.map(P, func); }
f.inverse = function (P) { return exports.GLM.utils.map(P, inv); }
f.derivative = function (P) { return exports.GLM.utils.map(P, deriv); }
return f;
};
exports.GLM.links.Logit = function () {
var f = function (P) { return exports.GLM.utils.map(P, function (p) { return Math.log(p / (1.0 - p)); }) };
f.inverse = function (P) { return exports.GLM.utils.map(P, function (p) { var t = Math.exp(p); return t / (1.0 + t); }); };
f.derivative = function (P) { return exports.GLM.utils.map(P, function (p) { return 1.0 / (p * (1.0 - p)); }); };
return f;
};
exports.GLM.links.Power = function (power) {
var f = function (P) { return exports.GLM.utils.map(P, function (p) { return Math.pow(p, power); }); }
f.inverse = function (P) { return exports.GLM.utils.map(P, function (p) { return Math.pow(p, 1.0 / power); }); }
f.derivative = function (P) { return exports.GLM.utils.map(P, function (p) { return power * Math.pow(p, power - 1); }); }
return f;
};
exports.GLM.links.Identity = function () {
return exports.GLM.links.Power(1.0);
};
exports.GLM.links.Log = function () {
var f = function (P) { return exports.GLM.utils.map(P, Math.log); }
f.inverse = function (P) { return exports.GLM.utils.map(P, Math.exp); }
f.derivative = function (P) { return exports.GLM.utils.map(P, function (p) { return 1.0 / p; }); }
return f;
};
exports.GLM.links.NegativeBinomial = function (alpha) {
var f = function (P) {
return exports.GLM.utils.map(P, function (p) { return Math.log(p / (p + 1.0 / alpha)); });
};
f.inverse = function (P) {
return exports.GLM.utils.map(P, function (p) { return Math.exp(p) / (alpha * (1 - Math.exp(p))); });
}
f.derivative = function (P) {
return exports.GLM.utils.map(P, function (p) { return 1.0 / (p + alpha * Math.pow(p, 2)); });
}
return f;
};
exports.GLM.optimization = exports.optimization || {};
/* TODO: this is incomplete
exports.optimization.CoordinateDescentPenalizedWeightedLeastSquares = function (endogenous, exogenous, gradientFunction, regularizationParameter, elasticnetParameter, maxIterations) {
// initialize defaults
if (!regularizationParameter) { regularizationParameter = 0.01; }
if (!elasticnetParameter) { elasticnetParameter = 0.5; } // defaults to half lasso, half ridge
if (!maxIterations) { maxIterations = 1000; }
var converged = false,
iteration = 0,
n_features = endogenous[0].length;
weights = exports.GLM.utils.zeros(endogenous[0].length);
while (!converged) {
var currentFeatureId = iteration % n_features,
oldWeights = clone(weights),
gradient = gradientFunction(endogenous, exogenous, weights, currentFeatureId, regularizationParameter, elasticnetParameter); // compute gradient along given axis
weights[currentFeatureId] = gradient;
iteration += 1;
converged = exports.GLM.utils.checkConvergence(weights, oldWeights, iteration, maxIterations);
}
return weights;
};
*/
exports.GLM.optimization.IRLS = function (endogenous,
exogenous,
family) {
var converged = false,
iterations = 0,
maxIterations = 5,
mu = family.initialMu(endogenous),
eta = family.predict(mu),
deviance = family.deviance(endogenous, mu),
wlsResults = null,
dataWeights = exports.GLM.utils.makeArray(endogenous.length, 1);
while (!converged) {
var weights = exports.GLM.utils.mul(dataWeights, family.weights(mu));
oldDeviance = deviance;
var ddot = 0.0,
muprime = family.link.derivative(mu);
var wlsEndogenous = exports.GLM.utils.map(eta, function(x, i) { return x + muprime[i] * (endogenous[i] - mu[i]); });
wlsResults = exports.GLM.optimization.linearSolve(wlsEndogenous, exogenous, weights);
eta = exports.GLM.utils.dot(exogenous, wlsResults);
mu = family.fitted(eta);
deviance = family.deviance(endogenous, mu);
converged = exports.GLM.utils.checkConvergence(deviance, oldDeviance, iterations, maxIterations);
iterations += 1;
}
return wlsResults;
};
exports.GLM.optimization.linearSolve = function (A, b, weights) {
// linear solver using Moore-Penrose pseudoinverse SVD method
function whiten(X, weights) {
if (exports.GLM.utils.isArray(X[0])) {
// 2d matrix
return exports.GLM.utils.map(weights, function (w, i) { return exports.GLM.utils.map(X[i], function(z) { return Math.sqrt(w) * z; }); } );
} else {
return exports.GLM.utils.map(weights, function (w, i) { return Math.sqrt(w) * X[i]; });
}
}
A = whiten(A, weights);
b = whiten(b, weights);
/* solve Ax=b for x using svd pseudoinverse */
function project_and_invert(V) {
var id_matrix = exports.GLM.utils.identity(V.length);
for (var i = 0; i < V.length; i++) { id_matrix[i][i] /= V[i]; }
return id_matrix;
}
var decomposition = exports.GLM.thinsvd(exports.GLM.utils.dot(exports.GLM.utils.transpose(b), b)),
U = decomposition[0],
S_inverse = project_and_invert(decomposition[1]),
V = decomposition[2],
psuedoinv = exports.GLM.utils.dot(U, exports.GLM.utils.dot(S_inverse, exports.GLM.utils.inverse(V))),
solution = exports.GLM.utils.dot(exports.GLM.utils.dot(psuedoinv, exports.GLM.utils.transpose(b)), A);
return solution;
}
})(this);