Questions tagged [tensor]

In machine learning, tensor is a multidimensional (multi-index, or multi-way) array of numbers, i.e. a generalization of a matrix.

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Why the sudden fascination with tensors?

I've noticed lately that a lot of people are developing tensor equivalents of many methods (tensor factorization, tensor kernels, tensors for topic modeling, etc) I'm wondering, why is the world suddenly fascinated with tensors? Are there recent…
Y. S.
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Difference between samples, time steps and features in neural network

I am going through the following blog on LSTM neural network: http://machinelearningmastery.com/understanding-stateful-lstm-recurrent-neural-networks-python-keras/ The author reshapes the input vector X as [samples, time steps, features] for…
Vipul Jain
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Tensors in neural network literature: what's the simplest definition out there?

In the neural network literature, often we encounter the word "tensor". Is it different from a vector? And from a matrix? Have you got any specific example that clarifies its definition? I'm a bit confused about its definition. Wikipedia doesn't…
user_1177868
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"row" and "column" are the names of axes of 2d array, is there a similar naming for a 3d array?

row and column are the names of axes of 2d array. this python array, array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) could be viewed as a matrix that has 3 rows and 3 columns. first row is [0, 1, 2], first column is [0, 3, 6]. Is there a similar naming for…
whnlp
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Usage of tensor notation in statistics

A friend of mine (mathematician) basically told me I shouldn't bother with matrix algebra and should focus on tensor analysis/manipulation. He said it's much more general and intuitive. I've been trying to grasp most of the matrix literature…
user143074
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The meaning of tensors in the neural network community

In the neural network community, is a tensor pretty much always just a multi-dimensional array?
Franck Dernoncourt
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Higher order tensors in Statistics

I am looking for problems in Statistics or application areas in Statistics which deal with three-way data or higher order data or 3-Tensors. Is there a regression setting where the covariates are expressed as a higher order tensor instead of a…
hearse
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Proof of normal equation in regression using tensor notation

I'm struggling with a proof of the normal equation, so I posted a question which hopefully will get resolved soon. However, I mentioned there that I'm uncomfortable with the proofs dealing with matrix calculus , particularly when it comes to…
r_31415
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obtaining 4th moment tensor under change of coordinates

Suppose I have a random real-valued vector $x=x_1,\ldots,x_d$ and $M_{ijkl}=E[x_i x_j x_k x_l]$ and apply a change of coordinates $y=Ax$ where $A$ is an orthogonal matrix. How do I obtain $N_{ijkl}=E[y_i y_j y_k y_l]$ ?
Yaroslav Bulatov
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Intuition behind using tensors ?

I am trying to build a recommendation model by using a tensor. In order to recommend an article to a user, I have built a model to predict users' preferable articles. I am labeling articles based on topics, the result of my learning dataset is a…
user3378649
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Quantile gam (qgam) of tensor product using gratia: drawing a contour plot of the response rather than the partial effect

Let's imagine the quantile regression (qgam) of the tensor product below. library("mgcv") library("qgam") library("gratia") library("ggplot2") library("dplyr") library("geomtextpath") # qgam qg0 <- qgam(z0 ~ te(x0, y0, k=c(5,5), bs=c("cr","cr")),…
denis
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Constraint on te() tensor product gam mgcv

In the mgcv package in R, I'm working on models whose covariates are forced to change shape at the median (=0). These are the models: gam1 <- gam(Y~ s(X1, pc=0)+s(X2, pc=0), data=data) gam2 <- gam(Y~ te(X1, X2, pc=c(0,0)),data=data) Unfortunately,…
Tesla
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Einstein notation $-$ or another $-$ to denote constraints in high dimensional ILP problems

When discussing marginal sums of arrays in 3 dimensions or more, is it customary in the statistical and/or data science communities to use the Einstein summation convention? Is some other form preferred? The context is an integer linear programming…
Peter Leopold
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Higher moments of linear regression residuals?

I previously asked this on Math StackExchange , with no success, but this post will add to that with some simulations. Background In the following linear regression with i.i.d $\epsilon_i$ $(i = 1, \cdots, n)$ with mean 0 finite moments of all order…
Tom Chen
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Solve Least Square Problem of a Sum of $N$ Quadratic Forms with a Positive Vector

Suppose we are given a list of $N$ positive definite quadratic forms $X^TQ_k X$ (where $k\in[1,N]$ and $Q_k\in\mathbb{R}^{p\times p}$ $\forall k$ ), and a positive vector $V$ of same length $N$ i.e. $V=(v_k>0)_{k\in[1,N]}$ . My question is the…
Ernest F
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