def fit(
self, X_ptrs: List[torch.Tensor], C_ptrs: List[torch.Tensor], y_ptrs: List[torch.Tensor]
):
# Checking if the pointers are as expected
self._check_ptrs(X_ptrs, C_ptrs, y_ptrs)
# Check if each y is a 2-dim or 1-dim tensor, unsqueeze it if it's 1-dim
for i, y in enumerate(y_ptrs):
if len(y.shape) < 2:
y_ptrs[i] = y.unsqueeze(1)
self.workers = self._get_workers(X_ptrs)
# Computing aggregated pairwise dot products remotely
XX_ptrs, Xy_ptrs, yy_ptrs, CX_ptrs, Cy_ptrs = self._remote_dot_products(
X_ptrs, C_ptrs, y_ptrs
)
# Compute remote QR decompositions
R_ptrs = self._remote_qr(C_ptrs)
# Secred share tensors between hbc_worker, crypto_provider and a random worker
# and compute aggregates. It corresponds to the Combine stage of DASH's algorithm
idx = random.randint(0, len(self.workers) - 1)
XX_shared = sum(self._share_ptrs(XX_ptrs, idx))
Xy_shared = sum(self._share_ptrs(Xy_ptrs, idx))
yy_shared = sum(self._share_ptrs(yy_ptrs, idx))
CX_shared = sum(self._share_ptrs(CX_ptrs, idx))
Cy_shared = sum(self._share_ptrs(Cy_ptrs, idx))
R_cat_shared = torch.cat(self._share_ptrs(R_ptrs, idx), dim=0)
# QR decomposition of R_cat_shared
_, R_shared = qr(R_cat_shared, norm_factor=self.total_size ** (1 / 2))
# Compute inverse of upper matrix
R_shared_inv = self._inv_upper(R_shared)
Qy = R_shared_inv.t() @ Cy_shared
QX = R_shared_inv.t() @ CX_shared
denominator = XX_shared - (QX ** 2).sum(dim=0)
# Need the line below to perform inverse of a number in MPC
inv_denominator = ((0 * denominator + 1) / denominator).squeeze()
coef_shared = (Xy_shared - QX.t() @ Qy).squeeze() * inv_denominator
sigma2_shared = (
(yy_shared - Qy.t() @ Qy).squeeze() * inv_denominator - coef_shared ** 2
) / self._dgf
self.coef = coef_shared.get().float_precision()
self.sigma2 = sigma2_shared.get().float_precision()
self.se = self.sigma2 ** (1 / 2)
self._compute_pvalues()
def _remote_qr(C_ptrs):
"""
Performs the QR decompositions of permanent covariate matrices remotely.
It returns a list with the upper right matrices located in each worker
"""
R_ptrs = []
for c in C_ptrs:
_, r = qr(c)
R_ptrs.append(r)
return R_ptrs