Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [topologies]

19 questions
70
votes
3 answers

What's the difference between feed-forward and recurrent neural networks?

What is the difference between a feed-forward and recurrent neural network? Why would you use one over the other? Do other network topologies exist?
Shane
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13
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2 answers

Graphical intuition of statistics on a manifold

On this post, you can read the statement: Models are usually represented by points $\theta$ on a finite dimensional manifold. On Differential Geometry and Statistics by Michael K Murray and John W Rice these concepts are explained in prose…
Antoni Parellada
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9
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1 answer

Topologies for which the ensemble of probability distributions is complete

I have been struggling quite a bit with reconciling my intuitive understanding of probability distributions with the weird properties that almost all topologies on probability distributions possess. For example, consider a mixture random variable…
Guillaume Dehaene
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7
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1 answer

Laplacian-Beltrami approximation based on an empirical sample

Given a probability measure $\nu$ on a subset $M \subseteq \mathbb{R}^N$ we construct the corresponding operator $$L^tf(x)=f(x)\int_{M} e^{-\frac{||x-y||^2}{4t}}d\nu(y)-\int_{M}f(y)e^{-\frac{||x-y||^2}{4t}}d\nu(y).$$ Let data points $x_1, \dots,…
hearse
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6
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1 answer

2 hidden layers are more powerful than 1

When searching for information on choosing the number of hidden layers in a neural network, I have come across the following table mutiple times, including in this answer: | Number of Hidden Layers | Result | 0 - Only capable of representing linear…
user76284
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6
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1 answer

Cases where TDA outperforms public benchmarks?

Precise Question What are some specific examples where topological data analysis (TDA) outperforms other models on publicly available data? Context When new ML algorithms are developed, it seems common practice to apply them to publicly-available…
Quetzalcoatl
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4
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2 answers

Where can I get real data of big network topology?

I want to model how traffic will flow on real networks (not just the internet, also, say, Intel's internal LAN). Is there a place I can get real network topologies data I can use?
Elazar Leibovich
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4
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2 answers

In "A Topology Layer for Machine Learning," are the topological priors learned by the network or imposed by humans?

In this paper by Gabrielsson, Nelson, et al. the authors "present a differentiable topology layer that can, among other things, construct a loss on the output of a deep generative network to incorporate topological priors". I only have a basic…
kdbanman
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4
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1 answer

Topological rather than metric based machine learning theory?

The first notion of continuity in a math class is usually the one based on metric spaces. In particular, the $\epsilon,\delta$ definition of continuity. But in topology, a more general notion of continuity is defined. In the context of machine…
user56834
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4
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0 answers

Topology of Confidence Intervals

I hope this is the right site to post this. The example I have in my mind is a GLMM model, where we infer random effects, and a random effect caterpillar plot (with confidence intervals): Now, suppose we start applying topological data analysis…
Alex R.
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3
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Reference request: Network/graph topology inference

I am a mathematician looking for a survey/book on methods for inference of graph/network topology (structure). Specifically, the kind of problem I am looking to study is as follows: Given a graph $G$ consider an unknown function $f$ such that…
Rodrigo Zepeda
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3
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1 answer

Visualizing model trajectories for Neural Networks using function approximator

Erhan et al. in their 2010 paper discusses how pre-training improves deep networks: http://www.jmlr.org/papers/volume11/erhan10a/erhan10a.pdf#page=15 In there, they compare different neural network models by visualizing the function representation…
The Wanderer
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Analysis techiques for logical topologies

I'm working in the area of analysis of logical computer systems (e.g https://goo.gl/images/KyLCCo). Specifically in the field of anomaly detection of these systems. I was thinking about the field of spatial analysis where analysis is conducted on a…
Jonathan Dunne
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2
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How to identify manifolds for an optimisation problem

I don't have much experience in topology, but I am interested to know if: • Given a particular problem and associated cost function, how would one deduce what kind of manifold this problem lies on. I ask this because as far as I know standard…
tisPrimeTime
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Neural networks, mapping features to polar coordinates to deal with uncertain inputs

Let's say you've got a neural network which takes in a vector of real numbers as input. Additionally, let's say you're uncertain about the values of some components of the vector, and your level of certainty is a number between $0$ and $1$. It's a…
wlad
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