tensor-on-tensor regression: riemannian optimization, over-parameterization, statistical-computational gap and their interplay

1 answer:

7 0

The purpose of the tensor-on-tensor regression, which we examine, is to relate tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without being aware of its intrinsic rank beforehand.

By examining the impact of rank over-parameterization, we suggest the Riemannian Gradient Descent (RGD) and Riemannian Gauss-Newton (RGN) methods to address the problem of unknown rank. By demonstrating that RGD and RGN, respectively, converge linearly and quadratically to a statistically optimal estimate in both rank correctly-parameterized and over-parameterized scenarios, we offer the first convergence guarantee for the generic tensor-on-tensor regression. According to our theory, Riemannian optimization techniques automatically adjust to over-parameterization without requiring implementation changes.

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Solve for X -5x=45 A 225 B 9 C -9 D 45

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If the midpoint of two points is (2,5) and one of the endpoints is (6,3), what is the other endpoint?

aleksley [76]

To answer this question, you need to draw out the graph first. By doing so, you will be able to know where the other endpoint is located. (Fig. 1)

Next, count the number from the midpoint to the endpoint to determine the coordinates for the other endpoint. (Fig. 2)
Example: From (2, 5) to (6, 3)
x: 2 to 6 = 4 steps
y: 5 to 3 = 2 steps

From there, you can determine the other endpoint like this.
Example: From (2, 5) to the other endpoint
x: 2 to x1 = 4 steps
y: 5 to y1 = 2 steps

Therefore, x1 = -2 and y1 = 7
Other endpoint: (-2, 7)

Sorry for the messy drawing, it is hard to draw without a pen. Haha... hope this helps :)