Questions tagged [dimensions]
34 questions
38
votes
3 answers
Understanding input_shape parameter in LSTM with Keras
I'm trying to use the example described in the Keras documentation named "Stacked LSTM for sequence classification" (see code below) and can't figure out the input_shape parameter in the context of my data.
I have as input a matrix of sequences of…
mazieres
- 597
- 1
- 5
- 9
11
votes
4 answers
Estimating the dimension of a data set
A colleague in applied statistics sent me this:
"I was wondering if you know any way
to find out the true dimension of the
domain of a function. For example, a
circle is a one dimensional function
in a two dimensional space. If I do
…
user1157
3
votes
1 answer
Wilks' theorem when dimension of submodel is not well defined
Suppose $\{f(\cdot,\theta) : \theta \in \mathbb{R}^p\}$ is a statistical model satisfying the conditions for Wilks' theorem, and that we have a hypothesis test of the form:
$$H_0: \theta_p >0$$
$$H_1: \theta \in \mathbb{R}^p$$
Clearly, $H_0$ is a…
qwerty
- 33
- 2
3
votes
2 answers
Calculating multivariate integrals between lower and upper bounds
Suppose $\vec{X}=(x_1,x_2,...,x_n)$ follows some continuous multivariate distribution, such that $x_i\in{\rm I\!R}, i=1,...,n$.
Suppose also that I have access to the following functions:
$\phi(\vec{x})$, which gives me the pdf at point…
Felipe D.
- 218
- 1
- 7
3
votes
1 answer
Estimating dimensionality of feature space from distance matrix
I have a distance matrix with some noise (e.g. obtained by asking people how similar two objects from a set of objects are). I am interesting in finding the (best guess for the) dimensionality of the feature space for the objects (i.e. how many…
whatamess
- 151
- 1
3
votes
3 answers
Why correlation is not "transitive"?
First let me explain what I mean by "transitive"
Suppose that the price of product A and the price of product B has a correlation of .5
Suppose also that the price of product B and product C has a correlation of .5
One might thing that if…
Lay González
- 341
- 3
- 12
2
votes
1 answer
Why curse of dimensionality affects more non-parametric approaches?
I just want to know the reason why the curse of dimensionality mostly affects the non-parametric approaches compared with parametric ones.
olad uhg
- 21
- 1
2
votes
2 answers
Matrix and vectors, why different notation for dimensions?
If we collect data and put it into a matrix of size (100,3), we tend to say we have three-dimensional data. We think of each column as a dimension.
On the other side, if we have a vector of size (100,1), we tend to say this is a hundred-dimensional…
Stenga
- 241
- 2
- 10
2
votes
1 answer
Why aren't the coskewness and cokurtosis matrices square like the covariance matrix?
The variance-covariance matrix is shaped $p\times p$, whereas the co-skewness matrix is shaped $p\times p^2$ and the co-kurtosis matrix is $p\times p^3$. Why is this, given that skewness and kurtosis are merely the 3rd and 4th moments after…
develarist
- 3,009
- 8
- 31
2
votes
1 answer
What is a unit $n$-cube, and its connection to the support of a distribution?
In statistics, what is an intuitive way of saying what an $n$-cube is? how do support of distributions come to be defined by an $n$-cube? are $n$-cubes useful in any applications beyond being a descriptor of dimensionality?
develarist
- 3,009
- 8
- 31
2
votes
1 answer
Can't update bias using gradient descent, because derivative of loss function with respect to bias has different dimensions
I want to update a bias in my Neural Network using the gradient descent optimization algorithm. Unfortunately, the bias has different dimensions than the derivative of the loss function with respect to the bias. For example, the bias in the first…
mzmyslowski
- 43
- 5
1
vote
0 answers
How does t-SNE preserves embedding orders?
According to the triplet loss Wikipedia page:
t-SNE (t-distributed Stochastic Neighbor Embedding) preserves embedding orders via probability distributions, whereas triplet loss works directly on embedded distances.
From the Wikipedia page, I more…
Revolucion for Monica
- 753
- 4
- 17
1
vote
1 answer
Doubts on how to write in vector
I know I can write a vector like this: $\beta = ( \beta_{1}, \dots, \beta_{p})^{\top}$ and $\rho = (\rho_{1}, \dots, \rho_{q})^{\top}$ by this way it have dimension $p \times 1$ and $q \times 1$, respectively.
Sometimes someone writes this matrix…
Bruno
- 11
- 2
1
vote
1 answer
How do the units of the SIR model cancel out?
I was having trouble trying to understand the parameters of the simplest SIR model.
If beta is the effective contact rate and s is the percentage of people who are susceptible, then how do the units cancel out such that ds/dt is measured in…
Krishna Kalakkad
- 11
- 1
1
vote
0 answers
Checking if my categorical variables are really unidimensional, ordinal
I have 6 categorical variables that can have the values -1, 0 and +1. The extremes are assigned to a semantic label. During rating, the rater could select either one of the labels (-1, +1) or neither (0). For instance, one variable consists of the…
ruhig brauner
- 113
- 5