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2 years ago

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.

Learn more about tensor-on-tensor here

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Which is equivalent to 21.76 grams per minute?

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3 years ago

Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour.

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3 years ago

Point E has coordinates (-11, 7), and point F has coordinates (-5, 1). To the nearest unit, what is the distance between the two

Zigmanuir [339]

Answer:

8 units

Step-by-step explanation:

We can use the distance formula. Recall the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let (-11,7) be $x_1$ and $y_1$ , and (-5,1) be $x_2$ and $y_2$

Plug in the numbers:

$d=\sqrt{(-5-(-11))^2+(1-7)^2$

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3 years ago

Kyla put 4 ounces of milk in 2 cups of coffee for her parents. How much milk would she need for 16 cups of coffee?A: 1cB: 1qtC:2

Ronch [10]

Kyla put 4 ounces of milk in 2 cups of coffee for her parents. How much milk would she need for 16 cups of coffee?

A: 1c

B: 1qt

C:2c

D:2qt

______________

4 ounces of milk in 2 cups of coffee for her parents.

4/2= 2 ounces of milk per cup

___________________

for 16 cups

Do you know how many ounces correspond to c or qt?

16* 2= 32 ounces

________________

32 ounces = 1 qt

So then,

Kyla needs to put 1 qt for 16 cups of coffee

Answer: B 1 qt

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1 year ago