def compute(self, particles, particle_info, loss_fn):
diffs = jnp.expand_dims(particles, axis=0) - jnp.expand_dims(particles, axis=1)
if self._normed() and particles.ndim == 2:
diffs = safe_norm(diffs, ord=2, axis=-1) # N x D -> N
diffs = jnp.reshape(diffs, (diffs.shape[0] * diffs.shape[1], -1)) # N * N (x D)
factor = self.bandwidth_factor(particles.shape[0])
if diffs.ndim == 2:
diff_norms = safe_norm(diffs, ord=2, axis=-1)
else:
diff_norms = diffs
bandwidth = jnp.median(diff_norms) ** 2 * factor + 1e-5
def kernel(x, y):
diff = safe_norm(x - y, ord=2) if self._normed() and x.ndim >= 1 else x - y
kernel_res = jnp.exp(-(diff**2) / bandwidth)
if self._mode == "matrix":
if self.matrix_mode == "norm_diag":
return kernel_res * jnp.identity(x.shape[0])
else:
return jnp.diag(kernel_res)
else:
return kernel_res
return kernel
def compute(self, particles, particle_info, loss_fn):
if self._random_weights is None:
raise RuntimeError(
"The `.init` method should be called first to initialize the"
" random weights, biases and subset indices."
)
if particles.shape != self._random_weights.shape:
raise ValueError(
"Shapes of `particles` and the random weights are mismatched, got {}"
" and {}.".format(particles.shape, self._random_weights.shape)
)
factor = self.bandwidth_factor(particles.shape[0])
if self.bandwidth_subset is not None:
particles = particles[self._bandwidth_subset_indices]
diffs = jnp.expand_dims(particles, axis=0) - jnp.expand_dims(
particles, axis=1
) # N x N x D
if particles.ndim == 2:
diffs = safe_norm(diffs, ord=2, axis=-1) # N x N x D -> N x N
diffs = jnp.reshape(diffs, (diffs.shape[0] * diffs.shape[1], -1)) # N * N x 1
if diffs.ndim == 2:
diff_norms = safe_norm(diffs, ord=2, axis=-1)
else:
diff_norms = diffs
median = jnp.argsort(diff_norms)[int(diffs.shape[0] / 2)]
bandwidth = jnp.abs(diffs)[median] ** 2 * factor + 1e-5
def feature(x, w, b):
return jnp.sqrt(2) * jnp.cos((x @ w + b) / bandwidth)
def kernel(x, y):
ws = (
self._random_weights
if self.random_indices is None
else self._random_weights[self.random_indices]
)
bs = (
self._random_biases
if self.random_indices is None
else self._random_biases[self.random_indices]
)
return jnp.sum(
jax.vmap(lambda w, b: feature(x, w, b) * feature(y, w, b))(ws, bs)
)
return kernel
def kernel(x, y):
diff = safe_norm(x - y, ord=2) if self._normed() and x.ndim >= 1 else x - y
kernel_res = jnp.exp(-(diff**2) / bandwidth)
if self._mode == "matrix":
if self.matrix_mode == "norm_diag":
return kernel_res * jnp.identity(x.shape[0])
else:
return jnp.diag(kernel_res)
else:
return kernel_res
def test_safe_norm(axis, ord):
m = np.array([[1.0e-5, 2e-5, 3e-5], [-1e-5, 1e-5, 0]])
assert_allclose(
safe_norm(m, axis=axis),
jnp.linalg.norm(
m + (1e-5**ord if axis is None and ord is not None else 0.0),
ord=ord,
axis=axis,
),
atol=1e-4,
)
def kernel(x, y):
diff = safe_norm(x - y, ord=2, axis=-1) if self._mode == "norm" else x - y
return (self.const**2 + diff**2) ** self.expon