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bpa.js
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bpa.js
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import Matrix from '../util/matrix.js'
/**
* Budgeted online Passive-Aggressive
*/
export default class BPA {
// Online Passive-Aggressive Algorithms on a Budget
// http://proceedings.mlr.press/v9/wang10b/wang10b.pdf
/**
* @param {number} [c] Regularization parameter
* @param {number} [b] Budget size
* @param {'simple' | 'projecting' | 'nn'} [version] Version
* @param {'gaussian' | 'polynomial' | { name: 'gaussian', s?: number } | { name: 'polynomial', d?: number } | function (number[], number[]): number} [kernel] Kernel name
*/
constructor(c = 1, b = 10, version = 'simple', kernel = 'gaussian') {
this._c = c
this._b = b
this._version = version
if (typeof kernel === 'function') {
this._kernel = kernel
} else {
if (typeof kernel === 'string') {
kernel = { name: kernel }
}
switch (kernel.name) {
case 'gaussian':
this._s = kernel.s ?? 1
this._kernel = (a, b) =>
Math.exp(-(a.reduce((s, v, i) => s + (v - b[i]) ** 2, 0) ** 2) / this._s ** 2)
break
case 'polynomial':
this._d = kernel.d ?? 2
this._kernel = (a, b) => (1 + a.reduce((s, v, i) => s + v * b[i])) ** this._d
break
}
}
this._sv = []
this._nn = 1
}
/**
* Fit model.
*
* @param {Array<Array<number>>} x Training data
* @param {Array<1 | -1>} y Target values
*/
fit(x, y) {
for (let t = 0; t < x.length; t++) {
let s = 0
for (let k = 0; k < this._sv.length; k++) {
const sk = this._sv[k]
s += sk.a * this._kernel(x[t], sk.x)
}
const hl = Math.max(0, 1 - y[t] * s)
if (hl === 0) {
continue
}
const at = y[t] * Math.min(this._c, hl / x[t].reduce((s, v) => s + v ** 2, 0))
if (this._sv.length < this._b) {
this._sv.push({ x: x[t], a: at })
continue
}
if (this._version === 'simple') {
const ktt = this._kernel(x[t], x[t])
const tau = Math.min(this._c, hl / ktt)
let min_q = (at ** 2 * ktt) / 2 + this._c * hl
let r_star = -1
let beta_t = -1
for (let r = 0; r < this._sv.length; r++) {
const sk = this._sv[r]
const krt = this._kernel(sk.x, x[t])
const beta = (sk.a * krt) / ktt + tau * y[t]
const sr = s - sk.a * krt + beta * ktt
const q =
(sk.a ** 2 * this._kernel(sk.x, sk.x) + beta ** 2 * ktt - 2 * sk.a * beta * krt) / 2 +
this._c * Math.max(0, 1 - y[t] * sr)
if (q < min_q) {
min_q = q
r_star = r
beta_t = beta
}
}
if (r_star >= 0) {
this._sv.splice(r_star, 1)
this._sv.push({ x: x[t], a: beta_t })
}
} else if (this._version === 'projecting') {
const Kall = new Matrix(this._sv.length + 1, this._sv.length + 1)
for (let r = 0; r < this._sv.length; r++) {
Kall.set(r, r, this._kernel(this._sv[r].x, this._sv[r].x))
for (let q = 0; q < r; q++) {
const kv = this._kernel(this._sv[r].x, this._sv[q].x)
Kall.set(r, q, kv)
Kall.set(q, r, kv)
}
const kt = this._kernel(this._sv[r].x, x[t])
Kall.set(r, this._sv.length, kt)
Kall.set(this._sv.length, r, kt)
}
Kall.set(this._sv.length, this._sv.length, this._kernel(x[t], x[t]))
let min_q = Infinity
let r_star = -1
let best_beta = null
for (let r = 0; r < Kall.rows; r++) {
const K = Kall.copy()
K.remove(r, 0)
const Kr = K.col(r)
const Kt = K.col(this._sv.length)
K.remove(r, 1)
const Kinv = K.inv()
const sk = r < this._sv.length ? this._sv[r] : { x: x[t], a: at }
const Kinvkr = Kinv.dot(Kr)
const Kinvkt = Kinv.dot(Kt)
const tau = Math.min(
this._c,
Math.max(
0,
(1 - y[t] * (s - sk.a * Kall.at(r, this._sv.length) + sk.a * Kinvkr.tDot(Kt).toScaler())) /
Kinvkt.tDot(Kt).toScaler()
)
)
const beta = Matrix.mult(Kinvkr, sk.a)
beta.add(Matrix.mult(Kinvkt, y[t] * tau))
let q = sk.a ** 2 * Kall.at(r, r)
for (let i = 0; i < K.rows; i++) {
q += beta.at(i, 0) ** 2 * K.at(i, i)
for (let j = 0; j < i; j++) {
q += 2 * beta.at(i, 0) * beta.at(j, 0) * K.at(i, j)
}
q -= 2 * sk.a * beta.at(i, 0) * Kr.at(i, 0)
}
if (q < min_q) {
min_q = q
r_star = r
best_beta = beta
}
}
if (0 <= r_star && r_star < this._sv.length) {
this._sv.splice(r_star, 1)
this._sv.push({ x: x[t], a: 0 })
for (let i = 0; i < this._sv.length; i++) {
this._sv[i].a += best_beta.at(i, 0)
}
}
} else if (this._version === 'nn') {
const distances = Array.from({ length: this._sv.length + 1 }, () => [])
for (let r = 0; r < this._sv.length; r++) {
const sk = this._sv[r]
distances[r][r] = [Infinity, -1]
for (let k = 0; k < r && k < this._sv.length; k++) {
const d = sk.x.reduce((s, v, i) => s + (v - this._sv[k].x[i]) ** 2, 0)
distances[r][k] = [d, k]
distances[k][r] = [d, r]
}
distances[this._sv.length][r] = [x[t].reduce((s, v, i) => s + (v - sk.x[i]) ** 2, 0), r]
}
let min_q = Infinity
let r_star = -1
let best_beta = null
let nns = []
for (let r = 0; r <= this._sv.length; r++) {
const sk = r < this._sv.length ? this._sv[r] : { x: x[t], a: at }
distances[r].sort((a, b) => a[0] - b[0])
const nnidx = distances[r].map(v => v[1])
const K = new Matrix(this._nn + 1, this._nn + 1)
const Kr = new Matrix(this._nn + 1, 1)
for (let i = 0; i < this._nn; i++) {
K.set(i, i, this._kernel(this._sv[nnidx[i]].x, this._sv[nnidx[i]].x))
for (let j = 0; j < i; j++) {
const kij = this._kernel(this._sv[nnidx[i]].x, this._sv[nnidx[j]].x)
K.set(i, j, kij)
K.set(j, i, kij)
}
const kit = this._kernel(this._sv[nnidx[i]].x, x[t])
K.set(i, this._nn, kit)
K.set(this._nn, i, kit)
Kr.set(i, 0, this._kernel(sk.x, this._sv[nnidx[i]].x))
}
K.set(this._nn, this._nn, this._kernel(x[t], x[t]))
Kr.set(this._nn, 0, this._kernel(sk.x, x[t]))
const Kt = K.col(1)
const Kinv = K.inv()
const Kinvkr = Kinv.dot(Kr)
const Kinvkt = Kinv.dot(Kt)
const tau = Math.min(
this._c,
Math.max(
0,
(1 - y[t] * (s - sk.a * Kr.at(1, 0) + sk.a * Kinvkr.tDot(Kt).toScaler())) /
Kinvkt.tDot(Kt).toScaler()
)
)
const beta = Matrix.mult(Kinvkr, sk.a)
beta.add(Matrix.mult(Kinvkt, y[t] * tau))
let q = sk.a ** 2 * this._kernel(sk.x, sk.x)
for (let i = 0; i < K.rows; i++) {
q += beta.at(i, 0) ** 2 * K.at(i, i)
for (let j = 0; j < i; j++) {
q += 2 * beta.at(i, 0) * beta.at(j, 0) * K.at(i, j)
}
q -= 2 * sk.a * beta.at(i, 0) * Kr.at(i, 0)
}
if (q < min_q) {
min_q = q
r_star = r
best_beta = beta
nns = nnidx.slice(0, this._nn)
}
}
if (0 <= r_star && r_star < this._sv.length) {
this._sv.splice(r_star, 1)
this._sv.push({ x: x[t], a: best_beta.at(this._nn, 0) })
for (let i = 0; i < nns.length; i++) {
this._sv[nns[i]].a += best_beta.at(i, 0)
}
}
}
}
}
/**
* Returns predicted values.
*
* @param {Array<Array<number>>} data Sample data
* @returns {(1 | -1)[]} Predicted values
*/
predict(data) {
const pred = []
for (let i = 0; i < data.length; i++) {
let s = 0
for (let k = 0; k < this._sv.length; k++) {
const sk = this._sv[k]
s += sk.a * this._kernel(data[i], sk.x)
}
pred[i] = s < 0 ? -1 : 1
}
return pred
}
}