// Creates the features from the inputs. Features must be nSamples x nFeatures or nil
func FeaturizeTrainable(t Trainable, inputs common.RowMatrix, featurizedInputs *mat64.Dense) *mat64.Dense {
nSamples, nDim := inputs.Dims()
if featurizedInputs == nil {
nFeatures := t.NumFeatures()
featurizedInputs = mat64.NewDense(nSamples, nFeatures, nil)
}
rowViewer, isRowViewer := inputs.(mat64.RawRowViewer)
var f func(start, end int)
if isRowViewer {
f = func(start, end int) {
featurizer := t.NewFeaturizer()
for i := start; i < end; i++ {
featurizer.Featurize(rowViewer.RawRowView(i), featurizedInputs.RawRowView(i))
}
}
} else {
f = func(start, end int) {
featurizer := t.NewFeaturizer()
input := make([]float64, nDim)
for i := start; i < end; i++ {
inputs.Row(input, i)
featurizer.Featurize(input, featurizedInputs.RawRowView(i))
}
}
}
common.ParallelFor(nSamples, common.GetGrainSize(nSamples, minGrain, maxGrain), f)
return featurizedInputs
}
func (k *KMeans) Train(inputs *common.RowMatrix) {
nSamples, inputDim := inputs.Dims()
centroids := make([][]float64, k.Clusters)
// Assign the centroids to random data point to start
perm := rand.Perm(nSamples)
for i := 0; i < k.Clusters; i++ {
data := make([]float64, inputDim)
idx := perm[i]
inputs.Row(data, idx)
centroids[i] = data
}
distances := mat64.NewDense(nSamples, k.Clusters, nil)
row := make([]float64, inputDim)
for i := 0; i < nSamples; i++ {
inputs.Row(row, i)
for j := 0; j < k.Clusters; j++ {
d := floats.Distance(row, centroids[j])
distances.Set(i, j, d)
}
}
}
// TestLinearsolveAndDeriv compares the optimal weights found from gradient-based optimization with those found
// from computing a linear solve
func TestLinearsolveAndDeriv(t *testing.T, linear train.LinearTrainable, inputs, trueOutputs common.RowMatrix, name string) {
// Compare with no weights
rows, cols := trueOutputs.Dims()
predOutLinear := mat64.NewDense(rows, cols, nil)
parametersLinearSolve := train.LinearSolve(linear, nil, inputs, trueOutputs, nil, nil)
linear.SetParameters(parametersLinearSolve)
linear.Predictor().PredictBatch(inputs, predOutLinear)
//fmt.Println("Pred out linear", predOutLinear)
linear.RandomizeParameters()
parameters := linear.Parameters(nil)
batch := train.NewBatchGradBased(linear, true, inputs, trueOutputs, nil, loss.SquaredDistance{}, regularize.None{})
problem := batch
settings := multivariate.DefaultSettings()
settings.GradAbsTol = 1e-11
//settings. = 0
result, err := multivariate.OptimizeGrad(problem, parameters, settings, nil)
if err != nil {
t.Errorf("Error training: %v", err)
}
parametersDeriv := result.Loc
deriv := make([]float64, linear.NumParameters())
loss1 := batch.ObjGrad(parametersDeriv, deriv)
linear.SetParameters(parametersDeriv)
predOutDeriv := mat64.NewDense(rows, cols, nil)
linear.Predictor().PredictBatch(inputs, predOutDeriv)
linear.RandomizeParameters()
init2 := linear.Parameters(nil)
batch2 := train.NewBatchGradBased(linear, true, inputs, trueOutputs, nil, loss.SquaredDistance{}, regularize.None{})
problem2 := batch2
result2, err := multivariate.OptimizeGrad(problem2, init2, settings, nil)
parametersDeriv2 := result2.Loc
//fmt.Println("starting deriv2 loss")
deriv2 := make([]float64, linear.NumParameters())
loss2 := batch2.ObjGrad(parametersDeriv2, deriv2)
//fmt.Println("starting derivlin loss")
derivlinear := make([]float64, linear.NumParameters())
lossLin := batch2.ObjGrad(parametersLinearSolve, derivlinear)
_ = loss1
_ = loss2
_ = lossLin
/*
fmt.Println("param deriv 1 =", parametersDeriv)
fmt.Println("param deriv2 =", parametersDeriv2)
fmt.Println("linear params =", parametersLinearSolve)
fmt.Println("deriv1 loss =", loss1)
fmt.Println("deriv2 loss =", loss2)
fmt.Println("lin loss =", lossLin)
fmt.Println("deriv =", deriv)
fmt.Println("deriv2 =", deriv2)
fmt.Println("linderiv =", derivlinear)
//fmt.Println("Pred out deriv", predOutDeriv)
*/
/*
for i := 0; i < rows; i++ {
fmt.Println(predOutLinear.RowView(i), predOutBatch.RowView(i))
}
*/
if !floats.EqualApprox(parametersLinearSolve, parametersDeriv, 1e-8) {
t.Errorf("Parameters don't match for gradient based and linear solve.")
//for i := range parametersDeriv {
// fmt.Printf("index %v: Deriv = %v, linsolve = %v, diff = %v\n", i, parametersDeriv[i], parametersLinearSolve[i], parametersDeriv[i]-parametersLinearSolve[i])
//}
}
}
// TestPredict tests that predict returns the expected value, and that calling predict in parallel
// also works
func TestPredictAndBatch(t *testing.T, p Predictor, inputs, trueOutputs common.RowMatrix, name string) {
nSamples, inputDim := inputs.Dims()
if inputDim != p.InputDim() {
panic("input Dim doesn't match predictor input dim")
}
nOutSamples, outputDim := trueOutputs.Dims()
if outputDim != p.OutputDim() {
panic("outpuDim doesn't match predictor outputDim")
}
if nOutSamples != nSamples {
panic("inputs and outputs have different number of rows")
}
// First, test sequentially
for i := 0; i < nSamples; i++ {
trueOut := make([]float64, outputDim)
for j := 0; j < outputDim; j++ {
trueOut[j] = trueOutputs.At(i, j)
}
// Predict with nil
input := make([]float64, inputDim)
inputCpy := make([]float64, inputDim)
for j := 0; j < inputDim; j++ {
input[j] = inputs.At(i, j)
inputCpy[j] = inputs.At(i, j)
}
out1, err := p.Predict(input, nil)
if err != nil {
t.Errorf(name + ": Error predicting with nil output")
return
}
if !floats.Equal(input, inputCpy) {
t.Errorf("%v: input changed with nil input for row %v", name, i)
break
}
out2 := make([]float64, outputDim)
for j := 0; j < outputDim; j++ {
out2[j] = rand.NormFloat64()
}
_, err = p.Predict(input, out2)
if err != nil {
t.Errorf("%v: error predicting with non-nil input for row %v", name, i)
break
}
if !floats.Equal(input, inputCpy) {
t.Errorf("%v: input changed with non-nil input for row %v", name, i)
break
}
if !floats.Equal(out1, out2) {
t.Errorf(name + ": different answers with nil and non-nil predict ")
break
}
if !floats.EqualApprox(out1, trueOut, 1e-14) {
t.Errorf("%v: predicted output doesn't match for row %v. Expected %v, found %v", name, i, trueOut, out1)
break
}
}
// Check that predict errors with bad sized arguments
badOuput := make([]float64, outputDim+1)
input := make([]float64, inputDim)
for i := 0; i < inputDim; i++ {
input[i] = inputs.At(0, i)
}
output := make([]float64, outputDim)
for i := 0; i < outputDim; i++ {
output[i] = trueOutputs.At(0, i)
}
_, err := p.Predict(input, badOuput)
if err == nil {
t.Errorf("Predict did not throw an error with an output too large")
}
if outputDim > 1 {
badOuput := make([]float64, outputDim-1)
_, err := p.Predict(input, badOuput)
if err == nil {
t.Errorf("Predict did not throw an error with an output too small")
}
}
badInput := make([]float64, inputDim+1)
_, err = p.Predict(badInput, output)
if err == nil {
t.Errorf("Predict did not err when input is too large")
}
if inputDim > 1 {
badInput := make([]float64, inputDim-1)
_, err = p.Predict(badInput, output)
if err == nil {
t.Errorf("Predict did not err when input is too small")
}
}
// Now, test batch
// With non-nil
inputCpy := &mat64.Dense{}
inputCpy.Clone(inputs)
predOutput, err := p.PredictBatch(inputs, nil)
if err != nil {
t.Errorf("Error batch predicting: %v", err)
}
if !inputCpy.Equals(inputs) {
t.Errorf("Inputs changed during call to PredictBatch")
}
predOutputRows, predOutputCols := predOutput.Dims()
if predOutputRows != nSamples || predOutputCols != outputDim {
t.Errorf("Dimension mismatch after predictbatch with nil input")
}
outputs := mat64.NewDense(nSamples, outputDim, nil)
_, err = p.PredictBatch(inputs, outputs)
pd := predOutput.(*mat64.Dense)
if !pd.Equals(outputs) {
t.Errorf("Different outputs from predict batch with nil and non-nil")
}
badInputs := mat64.NewDense(nSamples, inputDim+1, nil)
_, err = p.PredictBatch(badInputs, outputs)
if err == nil {
t.Error("PredictBatch did not err when input dim too large")
}
badInputs = mat64.NewDense(nSamples+1, inputDim, nil)
_, err = p.PredictBatch(badInputs, outputs)
if err == nil {
t.Errorf("PredictBatch did not err with row mismatch")
}
badOuputs := mat64.NewDense(nSamples, outputDim+1, nil)
_, err = p.PredictBatch(inputs, badOuputs)
if err == nil {
t.Errorf("PredictBatch did not err with output dim too large")
}
}
// NewBatchGradBased creates a new batch grad based with the given inputs
func NewBatchGradBased(trainable Trainable, cacheFeatures bool, inputs, outputs common.RowMatrix, weights []float64, losser loss.DerivLosser, regularizer regularize.Regularizer) *BatchGradBased {
var features *mat64.Dense
if cacheFeatures {
features = FeaturizeTrainable(trainable, inputs, nil)
}
// TODO: Add in error checking
if losser == nil {
losser = loss.SquaredDistance{}
}
if regularizer == nil {
regularizer = regularize.None{}
}
if weights != nil {
// TODO: Fix weights
panic("non-nil weights")
}
nTrain, outputDim := outputs.Dims()
_, inputDim := inputs.Dims()
g := &BatchGradBased{
t: trainable,
inputs: inputs,
outputs: outputs,
features: features,
losser: losser,
regularizer: regularizer,
nTrain: nTrain,
outputDim: outputDim,
inputDim: inputDim,
nParameters: trainable.NumParameters(),
grainSize: trainable.GrainSize(),
}
// TODO: Add in row viewer stuff
// TODO: Create a different function for computing just the loss
//inputRowViewer, ok := inputs.(mat64.RowViewer)
//outputRowViewer, ok := outputs.(mat64.RowViewer)
// TODO: Move this to its own function
var f func(start, end int, c chan lossDerivStruct, parameters []float64)
switch {
default:
panic("Shouldn't be here")
case cacheFeatures:
f = func(start, end int, c chan lossDerivStruct, parameters []float64) {
lossDeriver := g.t.NewLossDeriver()
prediction := make([]float64, g.outputDim)
dLossDPred := make([]float64, g.outputDim)
dLossDWeight := make([]float64, g.nParameters)
totalDLossDWeight := make([]float64, g.nParameters)
var loss float64
output := make([]float64, g.outputDim)
for i := start; i < end; i++ {
// Compute the prediction
lossDeriver.Predict(parameters, g.features.RawRowView(i), prediction)
// Compute the loss
g.outputs.Row(output, i)
loss += g.losser.LossDeriv(prediction, output, dLossDPred)
// Compute the derivative
lossDeriver.Deriv(parameters, g.features.RawRowView(i), prediction, dLossDPred, dLossDWeight)
floats.Add(totalDLossDWeight, dLossDWeight)
}
// Send the value back on the channel
c <- lossDerivStruct{
loss: loss,
deriv: totalDLossDWeight,
}
}
case !cacheFeatures:
f = func(start, end int, c chan lossDerivStruct, parameters []float64) {
lossDeriver := g.t.NewLossDeriver()
prediction := make([]float64, g.outputDim)
dLossDPred := make([]float64, g.outputDim)
dLossDWeight := make([]float64, g.nParameters)
totalDLossDWeight := make([]float64, g.nParameters)
var loss float64
output := make([]float64, g.outputDim)
input := make([]float64, g.inputDim)
features := make([]float64, g.t.NumFeatures())
featurizer := g.t.NewFeaturizer()
for i := start; i < end; i++ {
g.inputs.Row(input, i)
featurizer.Featurize(input, features)
// Compute the prediction
lossDeriver.Predict(parameters, features, prediction)
// Compute the loss
g.outputs.Row(output, i)
loss += g.losser.LossDeriv(prediction, output, dLossDPred)
// Compute the derivative
lossDeriver.Deriv(parameters, features, prediction, dLossDPred, dLossDWeight)
// Add to the total derivative
floats.Add(totalDLossDWeight, dLossDWeight)
// Send the value back on the channel
c <- lossDerivStruct{
loss: loss,
deriv: totalDLossDWeight,
}
}
}
}
g.lossDerivFunc = f
return g
}
func BatchPredict(batch BatchPredictor, inputs common.RowMatrix, outputs common.MutableRowMatrix, inputDim, outputDim int, grainSize int) (common.MutableRowMatrix, error) {
// TODO: Add in something about error
// Check that the inputs and outputs are the right sizes
nSamples, dimInputs := inputs.Dims()
if inputDim != dimInputs {
return outputs, errors.New("predict batch: input dimension mismatch")
}
if outputs == nil {
outputs = mat64.NewDense(nSamples, outputDim, nil)
} else {
nOutputSamples, dimOutputs := outputs.Dims()
if dimOutputs != outputDim {
return outputs, errors.New("predict batch: output dimension mismatch")
}
if nSamples != nOutputSamples {
return outputs, errors.New("predict batch: rows mismatch")
}
}
// Perform predictions in parallel. For each parallel call, form a new predictor so that
// memory allocations are saved and no race condition happens.
// If the input and/or output is a RowViewer, save time by avoiding a copy
inputRVer, inputIsRowViewer := inputs.(mat64.RawRowViewer)
outputRVer, outputIsRowViewer := outputs.(mat64.RawRowViewer)
var f func(start, end int)
// wrapper function to allow parallel prediction. Uses RowView if the type has it
switch {
default:
panic("Shouldn't be here")
case inputIsRowViewer, outputIsRowViewer:
f = func(start, end int) {
p := batch.NewPredictor()
for i := start; i < end; i++ {
p.Predict(inputRVer.RawRowView(i), outputRVer.RawRowView(i))
}
}
case inputIsRowViewer && !outputIsRowViewer:
f = func(start, end int) {
p := batch.NewPredictor()
output := make([]float64, outputDim)
for i := start; i < end; i++ {
outputs.Row(output, i)
p.Predict(inputRVer.RawRowView(i), output)
outputs.SetRow(i, output)
}
}
case !inputIsRowViewer && outputIsRowViewer:
f = func(start, end int) {
p := batch.NewPredictor()
input := make([]float64, inputDim)
for i := start; i < end; i++ {
inputs.Row(input, i)
p.Predict(input, outputRVer.RawRowView(i))
}
}
case !inputIsRowViewer && !outputIsRowViewer:
f = func(start, end int) {
p := batch.NewPredictor()
input := make([]float64, inputDim)
output := make([]float64, outputDim)
for i := start; i < end; i++ {
inputs.Row(input, i)
outputs.Row(output, i)
p.Predict(input, output)
outputs.SetRow(i, output)
}
}
}
common.ParallelFor(nSamples, grainSize, f)
return outputs, nil
}
// LinearSolve trains a Linear algorithm.
// Assumes inputs and outputs are already scaled
// If features is nil will call featurize
// Will return nil if regularizer is not a linear regularizer
// Is destructive if any of the weights are zero
// Losser is always the two-norm
// Does not set the value of the parameters (in case this is called in parallel with a different routine)
func LinearSolve(linearTrainable LinearTrainable, features *mat64.Dense, inputs, trueOutputs common.RowMatrix,
weights []float64, regularizer regularize.Regularizer) (parameters []float64) {
// TODO: Allow tikhonov regularization
// TODO: Add test for weights
// TODO: Need to do something about returning a []float64
if !IsLinearSolveRegularizer(regularizer) {
return nil
}
if features == nil {
features = FeaturizeTrainable(linearTrainable, inputs, features)
}
_, nFeatures := features.Dims()
var weightedFeatures, weightedOutput *mat64.Dense
fmt.Println("In linear solve")
if weights != nil {
panic("Need functionality to be better. Either banded special case in matrix or do the mulitplication by hand")
scaledWeight := make([]float64, len(weights))
for i, weight := range weights {
scaledWeight[i] = math.Sqrt(weight)
}
diagWeight := diagonal.NewDiagonal(len(scaledWeight), scaledWeight)
nSamples, outputDim := trueOutputs.Dims()
weightedOutput = mat64.NewDense(nSamples, outputDim, nil)
weightedFeatures = mat64.NewDense(nSamples, nFeatures, nil)
weightedOutput.Copy(trueOutputs)
weightedFeatures.Copy(features)
// TODO: Replace this with better than mat multiply
weightedOutput.Mul(diagWeight, weightedOutput)
weightedFeatures.Mul(diagWeight, weightedFeatures)
}
switch regularizer.(type) {
case nil:
case regularize.None:
default:
panic("Shouldn't be here. Must be error in IsLinearRegularizer")
}
if weights == nil {
parameterMat, err := mat64.Solve(features, trueOutputs)
if err != nil {
panic(err)
}
return parameterMat.RawMatrix().Data
}
parameterMat, err := mat64.Solve(weightedFeatures, weightedOutput)
if err != nil {
panic(err)
}
return parameterMat.RawMatrix().Data
}