1

我有一个数据集——X由 15 个变量和 64 个观察值和一个列向量——Y代表目标（标签）的 64 个值组成。我尝试Y使用 PyTorch 将参数拟合到二次函数以返回观察值 ( )，但出现错误。我在文章末尾以 json 格式提供了数据集，以实现可重复性。

如果我有一个示例，我的代码可能是：

X = torch.from_numpy(X)
X.requires_grad = True
W = np.random.randn(15,15)
W = np.triu(W, k=0)
W = torch.from_numpy(W)
W.requires_grad = True

# define parameters for gradient descent
max_iter=100
lr_rate = 1e-3

# we will do gradient descent for max_iter iteration 
for i in range(max_iter):

        # compute the loss
        loss = Y - (X@torch.transpose(X, 1,0) * W).sum()
        # use torch.autograd.grad to compute the gradient
        W = W - lr_rate*torch.autograd.grad(out, W)[0]
        print(f"{i}: {out}")

您能否提供一个使用我在下面提供的数据以矢量化方式实现所述目标（将参数拟合到数据）的正确实现示例？

数据： X：

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是

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4

1 回答 1

0

我认为你的损失函数是错误的。目前，您已使用

loss = Y - (X@torch.transpose(X, 1,0) * W).sum()

理想情况下，由于我们使用 SGD 并试图最小化损失，我们希望当且仅当 Y 等于 时损失最小f(x)。但是，在您的情况下，损失会在尽可能f(x)大时最小化，然后Y-f(x)会尽可能小。y=f(x)请注意，当损失为正或负时，损失只会为 0 。一个快速的解决方法可能是让损失平方，这样它就永远是正的，只有当 时才为 0 y=f(x)。

loss = (Y - (X@torch.transpose(X, 1,0) * W).sum())**2

此外，如果Y,X是向量和矩阵（多个样本），您可以对损失求和或计算均值

loss = ((Y - (X@torch.transpose(X, 1,0) * W).sum())**2).mean()

于 2020-01-14T17:52:15.790 回答