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Questions tagged [machine-learning]

Questions about computer algorithms that automatically discover patterns in data and make good decisions based on them.

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How do you prove that a kernel trick can be used on a particular problem?

In the following SVM classifier optimisation problem, is there a way to show that a kernel trick can be used? I have tried showing that this fits the Representer theorem, however, I'm not sure how to ...
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13 views

Using ML to create artistic patterns

I know there are different projects that use neural networks to transform images from one style to another (Prisma being one of them), but are there anything one could use to create random patterns (...
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OR functions and SQ-Learning

Anyone can describe or give a reference which has a clear description and detailed proof of the SQ-Learning algorithm for the OR class of Boolean functions?
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11 views

About evaluation method of classification

I am still a beginner studying machine learning for the first time. I am dealing with problem of 4 class classification in my research. I would like to calculate accuracy, precision and recall. Since ...
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10 views

How should I represent an unordered set of dense vectors as input to a neural network?

My dataset consists of 10000 (x,y) pairs where x is an unordered set of 27-dimensional vectors with a total of 8 elements, and y is a different unordered set of 27-dimensional vectors with a total of ...
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Understanding the computational power of neural networks

It is known that a recurrent neural network with rational weights is computationally equivalent to a Turing Machine (a proof can be found in this paper). I don't understand how is it possible, it ...
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33 views

Proving Quadratic Kernel

We have the given quadratic kernel. $K(x, y) = (x^T y)^2$ $\phi([x1, x2]) = \{x1x1, x1x2, x2x1, x2x2\}$ Show that $K(x, y) = \phi(x)^T \phi(y)$ for arbitrary $n$-length vectors. I can show that ...
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6 views

A question on Relative Entropy Inverse Reinforcement Learning

I am reading Boularias' Relative Entropy Inverse Reinforcment learning (http://proceedings.mlr.press/v15/boularias11a/boularias11a.pdf) and I do not understand a paragraph of the premise of the method ...
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17 views

How can I represent the following mathematically? (Eigenfaces reconstrcution)

I got the following from a web site: The feature vectors represent each image as a linear combination of the eigenfaces defined by the coefficients in the feature vector; if we multiply each ...
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37 views

Card dealing problem with constraints (blacklisting),

A friend of mine and I are trying to teach a bot play a card game (bela) We are using monte carlo tree search (MCTS) to estimate the probability of winning hand in regards to multiple possible (!...
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1answer
49 views

(OCR ) How to Recognise Handwritten fractional numbers using Neural networks

I want to be able to recognise handwritten math numbers using images of the numbers , i was able to do create a ANN model for recognising simple decimal numbers , but i have no idea on how to ...
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1answer
83 views

Help needed for understanding proof of No Regret Multi Armed Bandit Algorithm

I was reading Elad Hazan's book on Online Convex Optimization(http://ocobook.cs.princeton.edu/OCObook.pdf) and am facing difficulty understanding the proof given for the No regret algorithm for MAB (...
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26 views

Explanation required about these Ghostly Images

I am reading the research paper “Eigen faces for Recognition”. Paper Link. In Figure 2, paper shows the seven Eigen faces having white and black spots on them. Is there any significance of these white ...
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1answer
30 views

Do data points mean Eigenfaces in higher dimensional space?

I saw the following animation at making sense of PCA , which shows blue data points. I am reading a paper on Eigenfaces which says that: "a typical image of size 256 by 256 becomes a vector of ...
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16 views

Neural network algorithm, finding weight gradient

I'm writing a neural network and am having trouble with finding the cost to weight gradient. Supposedly the gradient is given by $\frac{\partial C}{\partial w^l_{jk}} = a^{l-1}_k \partial^l_j$ but I'm ...
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20 views

Geometric algorithm which solve a cluster problem for high-dimensional data

Since I'm new in using geometric algorithms for machine learning, I hope to get help here. I'm looking for a topic for my thesis that deals with algorithms that solve cluster problems in high-...
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Machine learning for VLSI floorplanning tool

I have an educational assignment to make an VLSI floor-planning tool. Can I use machine learning in some part of the algorithm? For example, I was reading the book Algorithms for VLSI Physical Design ...
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43 views

Computational geometry in machine learning

So far, I have thought that an algorithm that solves a cluster problem, can be assigned to unsupervised learning, because clustering is part of machine learning. If I have now given an algorithm ...
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1answer
71 views

What is the difference in SMO algorithm for SVM and SMO for one class?

Please let know if this is not the correct forum to ask this question. If not can anyone please tell where can I ask this question? I am trying to understand the difference between the paper : https:/...
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1answer
29 views

Problem with Understanding “correlated attributes into a set of values of uncorrelated attributes” in PCA

I am studying PCA. I have a problem in understanding the following concept: What is meant by transforming "correlated attributes into a set of values of uncorrelated attributes" in Principal ...
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11 views

what is the variance of a linear regression estimator

Consider a linear regression model $$ Y=X\beta+\epsilon $$ and $$ \epsilon \sim N(0,\sigma^2I) $$ Given N training data(i.e. matrix X and Y). Assume $\hat{f}$ is the regression function. What is the ...
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12 views

Trouble with one line of the proof of PAC learning axis-aligned rectangles

The proof for PAC learning axis-aligned rectangles usally goes like this : Let $\mathsf{A}$ be the algorithm that constructs the tighest rectangle $\mathsf{R_S}$ containing all positive samples seen ...
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Is there an equivalent of “control flow” in deep learning systems?

Traditional programs work significantly through control flow. I know that there are simple algorithms that have no control flow at all (i.e. they just perform a fixed sequence of executions), but I ...
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4 views

Looking for a specific type of ADMM iterates

For a $k-$dimensional optimization variable $b \in \mathbb{R}^k$ say the objective is given as, $$f(b) = \langle b, v \rangle + \langle b , Ab \rangle + \lambda \Vert b \Vert_1$$ for some parameter ...
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Is the optimization of the Gaussian VAE well-posed?

In a Variational Autoencoder (VAE), given some data $x$ and latent variables $t$ with prior distribution $p(t) = \mathcal{N}(t | 0, I)$, the encoder aims to learn a distribution $q_{\phi}(t)$ that ...
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1answer
45 views

Show that the Laplace smoothing for bigrams is a valid probability distribution

If we consider any smoothing technique like laplace or delta smoothing. Intuitively we can see that the we are stealing from sequences with non zero probablity and re distribute to sequences with zero ...
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29 views

Proof of perceptron convergence theorem for ZERO threshold?

The generalized perceptron convergence theorem is for a defined threshold T. When you do the maths it all comes to an upper bound and a lower bound. The lower bound looks like this! Therefore ...
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19 views

Dimensionality Reduction to Find Abstract Concepts

I have a list of say 1000 topics and each are related to computer programming field such as if/else topic, while loop , for loop, integers, strings ect. I want to create a concept map for them which ...
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1answer
20 views

Checking if a kernel is valid

The kernel is $K(x,z) = \sum_{i=1}^D (x_i+z_i)$ My approach was trying to express $K = \phi(x)^T\phi(z) = (x_1 x_2 ... x_D \quad 1 1 ...1)(1 1 ...1\quad z_1 z_2 ... z_D )^T$ where $\phi$ is 2Dx1 ...
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39 views

What is the quantity sold for a specific fruit & country combination?

What is the algorithm that generates these potential quantities that meet the given criteria? Essentially - there are number of quantities for a fruit and country combination. E.g: ...
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9 views

Principle Component Analysis Help

My Attempt Part A: 1 dimension, and 2 dimensions for the PCs. Part B: Number of stations. Part C: not sure...
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1answer
34 views

Is Artificial General Intelligence possible with our current machine learning models? [closed]

In other words, is artificial human level intelligence not possible yet just because of limitations in processing power and amount of data required to train the models? Or we don't have the knowledge ...
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how many hidden layers in an n-layer neural network

Simple terminology question: (should be easy to answer) How many hidden layers does an n-layer neural network have? I believe the answer is n-1. For example a single layer perceptron has no hidden ...
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Applications of signed permutations to machine learning

Are there some applications of signed permutations to machine learning? I searched on google and only found one paper. Thank you very much.
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1answer
28 views

Matching/finding mathematical plot images

I'm trying to come up with a method to match a given mathematical plot against a database of other plots. To make it more specific: plots are generated in R as PNG and might have different dimensions. ...
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26 views

Random Forest: Differentiable or non-Differentiable Classifier?

I have read on a web site that differentiability is an important property for Machine Learning. Its link is: https://www.quora.com/Why-%E2%80%98differentiable%E2%80%99-is-the-most-important-keyword-in-...
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No free lunch theorem and finite hypothesis class contradiction?

I am currently learning machine learning thanks to this course : https://webdav.tuebingen.mpg.de/is-class-2/Lecture4.pdf I know that a finite hypothesis class $H$ is PAC-learnable. Let's say I take a ...
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36 views

Candidate Elimination Algorithm - Simple Problem

I'm trying to understand version space learning and the Candidate Elimination algorithm. Define the set of most general and the set of most specific hypotheses. Take these training examples with the ...
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14 views

momentum term in back propagation

back propagation with momentum term means we update the weights like so: $\Delta w_{i,j}(n)= \eta*\delta_j(n)*y_i(n)+\alpha*\Delta w_{i,j}(n-1) $ what do we intialize $\Delta w_{i,j}(0)$ to?
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1answer
24 views

Why doesn't this derivation of the margin in a SVM give the correct result?

I'm trying to derive the optimization objective for an SVM (namely $1/\|w\|$), but I'm running into a little trouble. I've already read this question, which has certainly offered a lot of insight into ...
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1answer
19 views

The notion of PAC in approximation algorithms

In computational machine learning, the notion of Probably Approximately Correct means that (generally speaking) we can find (or "learn") with a high probability a function which has "low error". Is ...
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1answer
17 views

Choose the best classifier to predict the label of strings of a regular language

I have to tackle this problem: I have some strings that are my training set. These strings belong to a regular language corresponding to a deterministic finite automata (hidden namely I don't now it, ...
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21 views

FastText how it works?

So my question is how Supervised FastText works for the most part. I understood in the original paper they use bag of n-grams for features, but then they released a paper with enriching the word ...
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1answer
93 views

Mathematical proof for why gradient descent algorithm always converges

I am currently learning machine learning and I stumbled across gradient descent. I understand why the algorithm always converges to the global/local minimum when the learning rate is small enough in ...
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23 views

What are good examples of computational theories for A.I. according to David Marr's Definition?

I was reading David Marr's "Artificial Intelligence-A Personal View" and he talks about "computational theory of AI" or what he laters labels as "Type 1" Theory. He provides the example of Chomsky's ...
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2answers
139 views

Does deep learning infer P = NP?

The question comes from the following scenario, assume we have the traveler problem which is NP (the one where a traveler wants to visit all countries with the lowest cost(by summing up all flights)) ...
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What is the “spatial information” in convolutional neural network

deep learning research papers always claim that deeper layers of CNN have good "semantic information" but poor "spatial information". What is the spatial information exactly. Is that some activations ...
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How to compute the loss and backprop of word2vec skip-gram using hierarchical softmax?

So we are calculating the loss $$J(\theta) = -\frac{1}{T}\sum_{t=1}^T\sum_{-m \leq j \leq m} \log P(w_{t+j}|w_t;\theta)$$ and to do this we need to calculate $$P(o|c) = \frac{\exp(u_o^Tv_c)}{\sum \...
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1answer
90 views

VC dimension of finite unions of one-sided intervals

What is the VC dimension of $k$ finite unions of one-sided intervals: If we take 3 one-sided intervals like $(-\infty, a_1] $, $(-\infty, a_2] $ and $(-\infty, a_3] $, I think union of these ...
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1answer
72 views

Cost of computational representation in PAC-learning definition

I'm currently reading Foundations of Machine Learning by M. Mohri, A. Rostamizadeh, A. Talwalkar and according to their definition a concept class $C$ is said to be PAC-learnable if $$Pr_{S \sim D^m}[...