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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Best way to present vectors/tensors with correlated elements
When analysing a molecular dynamics simulation, I get a tensor (3x3 matrix) at each timestep -- this is generally a function of the individual atomic positions in the simulation, $\mathbf{T}_i=f(\...
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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.
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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=...
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INDSCAL as a special case of CANDELINC
Here is my attempt to show that INDSCAL as a special case of CANDELINC. I am using the following paper as my reference for definitions.
Kolda, Tamara G., and Brett W. Bader. "Tensor ...
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How to implement and notate the replication/transformation of a 2D matrix to a 3D tensor and the summation/transformation of a 3D tensor to 2D matrix?
Background:
I have a model with a dimension $T$ representing $time$, a dimension $N$ representing $technologies$ and a dimension $P$ representing $prices$. During calculations in this model, I would ...
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te(x, by = factor) or s(x, by = factor)?
I'm trying to wrap my head around/put into words the meaning of an isotropic or anisotropic relation in the case of a linear term by factors (technical replicates). Would the use of s(x, by = factor) ...
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How to leverage the separable functions in MCMC sampling? [closed]
I'm considering the posterior of a parametric model via the Bayesian approach. More specificity, I have a parametric model $u(p_1,p_2, p_3) = u_1(p_1) \times u_2(p_2) \times u_3(p_3)$ and I want to ...
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Is the design matrix in a panel regression model a tensor?
In a panel regression model of the form
$$Y_{it} = \mathbf{X}_{it} \pmb{\beta} + \epsilon_{it}$$
where
$Y_{it}$ is the dependent variable for unit $i$ at time $t$
$\mathbf{X}_{it}$ is a vector of $K$ ...
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Is spiked tensor decomposition a special case of INDSCAL decomposition?
I understand that "Spiked" often refers to the presence of a dominant component (or a few dominant components) in a tensor decomposition. Spiked tensor decomposition is applied to multi-way ...
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Transformers: Cross Attention Tensor Shapes During Inference Mode
Using the "classic" transformer model describing in "Attention is All You Need", I'm struggling to understand how the Encoder output is used by the Decoder during cross attention ...
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How do continuous partial derivatives depend on $n$ in maximum likelihood estimation?
I'm reading Tensor Methods in Statistics by McCullagh 1987, (P209 for this question) and I can't understand one step he uses.
He begins with the usual log-likelihood
\begin{equation*}
l(\theta; Y) =...
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Difference between multi-head and single-head attention
Attention, as long as gradient calculations care, is two nested tensor multiplications and a softmax. I thought that, then, multi-head attention with $h=8$ and $d_k=64$ results in the same tensor with ...
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mgcv: Use of s() or te() with interactions in GAMs?
I am trying to model CO2 fluxes (fco2) using a number of environmental parameters using a GAM in mgcv.
Specifically, I have leaf temperature (tl), vapour pressure deficit (vpd), and soil water content ...
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Constaint 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:
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Better default prior for non-negative canonical polyadic decomposition of counts than Exp(1)?
Suppose I have a instance of a random $k$-mode tensor $X_{n_1 \times \ldots \times n_k}$ of count data. I would like to perform non-negative canonical polyadic decomposition of this tensor using ...
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