# Questions tagged [machine-learning]

Theoretical questions about Machine learning, especially Computational Learning Theory, including Algorithmic Learning Theory, PAC learning, and Bayesian Inference

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### How is the complexity of PCA $O(\min(p^3,n^3))$?

I've been reading a paper on Sparse PCA, which is: http://stats.stanford.edu/~imj/WEBLIST/AsYetUnpub/sparse.pdf And it states that, if you have $n$ data points, each represented with $p$ features, ...
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### Convergence of Q-learning with non-linear function approximation

Q-learning is a well-known algorithm in Reinforcement learning which enjoys great empirical success but with insufficient theoretical understanding. In the tabular setting, it is known that if each ...
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### Boolean functions with high query complexity for PAC learning

The most general theorem for PAC learning of Boolean functions that I am aware of is the theorem in section 3.4 of Ryan O'Donnel's book where its basically shown that Boolean functions whose Fourier ...
116 views

### Off-policy Monte Carlo Control

The off-policy Monte Carlo control algorithm to learn the optimal state-value function $V^*$ is given as follows, which is obtained from Sutton's book. I have three questions concerning this ...
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### Can the distribution over the squared moduli of the 'probabilities' defined by an RBM with complex weights be written as an RBM with real weights? [closed]

I posted this question originally on the math boards, but figured it would be better suited here. https://math.stackexchange.com/questions/2203967/can-the-distribution-over-the-squared-moduli-of-the-...
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### A well-known instance of overcomplete dictionaries

sparse representation is: A signal can be represented as a linear combination of basis functions where the set of basis functions is called dictionary and data samples are much more than their ...
36 views

### How to find a proper probabilistic formulation given the objective function terms?

I want to pose a problem as maximisation of MAP probability $P(X,Y|Z)$ and I know which terms I want to have in the objective function. However, I am unable to combine these terms to form a joint ...
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### Identifying ambiguities in inductively learned concepts

I'm looking at ways in which "ambiguities" can be identified in labeled training data by a system undergoing some sort of inductive learning process. Do you know if there is any literature on this ...
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### How to define deep learning? [closed]

Ive read some articles about deep learning but I found its hard to provide a clear definition of deep learning. For me its like an intelligent feature selection method. But it seems that its not ...
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### What's the meaning of the class indicator matrix when transforming the class label matrix into it in canonical correlation analysis?

When using canonical correlation analysis (CCA), we can integrate the dataset and label information via transforming the class label matrix Y into the class indicator matrix T. Such as: $T = (YY^T)^½Y$...
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### Generalization Issues with Practical Suggestions from Universal Approximation Theorem with Neural Networks

After having read matus's beautiful answer in this thread explaining (among other things) Cybenko's proof of the Universal Approximation Theorem for Neural Networks, I wonder: if we use a piecewise ...
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### How to find the shattering set size without visualising the target function behaviour?

My aim is to prove a vc-dimension $d$ for different problems. All the problems I have do not have visualised target function (or concept) . I know this is unnecessarily. But this unlike most of the ...
110 views

### Techniques to get nodes in the best Markov Cluster?

I was using Markov Clustering to cluster nodes in my bidirectional graph, and overall the results were great. However, there were a couple instances where a weakly connected node would attract a node ...
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### Belief Propagation on MRF with complex cliques

Is there a belief propagation algorithm for exact inference on a MRF with complex clique structures (i.e. ones involving more than 2 neighbours)? For MRF's with cliques that only involve pairwise ...
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### Derivation of Expected-Maximization training equations for a noisy-OR Bayesian network

How do I derive the EM training equations for a noisy-OR Bayesian network? I am familiar with one solution to these equations. If I remember correctly, the result is: Given a model with link ...
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### Using Graphs/Graph Similarity as Features for a Learner

I'm working to construct a learner than can recognize whether two vertices in a property graph (digraph, vertices and edges can have arbitrary keys/values) modelling a social network in fact represent ...