// Note: For small probabilities, product may end up zero due to underflow error. Can circumvent
// by taking logs.
@Override
protected double[] score0(double[] data, double[] preds) {
double[] nums = new double[_output._levels.length]; // log(p(x,y)) for all levels of y
assert preds.length
== (_output._levels.length + 1); // Note: First column of preds is predicted response class
// Compute joint probability of predictors for every response class
for (int rlevel = 0; rlevel < _output._levels.length; rlevel++) {
// Take logs to avoid overflow: p(x,y) = p(x|y)*p(y) -> log(p(x,y)) = log(p(x|y)) + log(p(y))
nums[rlevel] = Math.log(_output._apriori_raw[rlevel]);
for (int col = 0; col < _output._ncats; col++) {
if (Double.isNaN(data[col])) continue; // Skip predictor in joint x_1,...,x_m if NA
int plevel = (int) data[col];
double prob =
plevel < _output._pcond_raw.length
? _output._pcond_raw[col][rlevel][plevel]
: _parms._laplace
/ ((double) _output._rescnt[rlevel]
+ _parms._laplace
* _output
._domains[col]
.length); // Laplace smoothing if predictor level unobserved in
// training set
nums[rlevel] +=
Math.log(
prob <= _parms._eps_prob
? _parms._min_prob
: prob); // log(p(x|y)) = \sum_{j = 1}^m p(x_j|y)
}
// For numeric predictors, assume Gaussian distribution with sample mean and variance from
// model
for (int col = _output._ncats; col < data.length; col++) {
if (Double.isNaN(data[col])) continue; // Skip predictor in joint x_1,...,x_m if NA
double x = data[col];
double mean =
Double.isNaN(_output._pcond_raw[col][rlevel][0])
? 0
: _output._pcond_raw[col][rlevel][0];
double stddev =
Double.isNaN(_output._pcond_raw[col][rlevel][1])
? 1.0
: (_output._pcond_raw[col][rlevel][1] <= _parms._eps_sdev
? _parms._min_sdev
: _output._pcond_raw[col][rlevel][1]);
// double prob = Math.exp(new NormalDistribution(mean, stddev).density(data[col])); //
// slower
double prob =
Math.exp(-((x - mean) * (x - mean)) / (2. * stddev * stddev))
/ (stddev * Math.sqrt(2. * Math.PI)); // faster
nums[rlevel] += Math.log(prob <= _parms._eps_prob ? _parms._min_prob : prob);
}
}
// Numerically unstable:
// p(x,y) = exp(log(p(x,y))), p(x) = \Sum_{r = levels of y} exp(log(p(x,y = r))) -> p(y|x) =
// p(x,y)/p(x)
// Instead, we rewrite using a more stable form:
// p(y|x) = p(x,y)/p(x) = exp(log(p(x,y))) / (\Sum_{r = levels of y} exp(log(p(x,y = r)))
// = 1 / ( exp(-log(p(x,y))) * \Sum_{r = levels of y} exp(log(p(x,y = r))) )
// = 1 / ( \Sum_{r = levels of y} exp( log(p(x,y = r)) - log(p(x,y)) ))
for (int i = 0; i < nums.length; i++) {
double sum = 0;
for (int j = 0; j < nums.length; j++) sum += Math.exp(nums[j] - nums[i]);
preds[i + 1] = 1 / sum;
}
// Select class with highest conditional probability
preds[0] = GenModel.getPrediction(preds, _output._priorClassDist, data, defaultThreshold());
return preds;
}
