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Questions tagged [time-complexity]

Computational complexity (aka time complexity) of an algorithm is the amount of time it needs to run as a function of the input size.

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146 views

What is the computational complexity of a 1D convolutional layer?

What is the complexity of a 1D convolutional layer?. I'm getting $\mathcal{O}(n \cdot k \cdot d)$, but in Attention Is All You Need, Vaswani et al. report that it is $\mathcal{O}(k \cdot n \cdot d^2 )$...
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Complexity associated with decision trees

According to the sklearn documentation on decision trees: The cost of using the tree (i.e., predicting data) is logarithmic in the number of data points used to train the tree. Could somebody ...
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applying fast Fourier transform without restriction on N

I want to apply fast Fourier transform for a sequence of complex numbers with length N. N can be anything (not necessarily a power of 2). It seems that Cooley–Tukey algorithm only works for the ...
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Computational complexity in practice: predict execution time for a dataset

Suppose I know that the computational complexity of an algorithm is $\mathcal{O}(f(n))$ where $n$ is the sample size. Suppose I have two data sets with sizes $n_1$ and $n_2$. The data sets have no ...
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(Teaching) references for computational complexity

Background: I am going to teach computational complexity (time complexity) within an introductory course in machine learning. I would like to gently introduce the notion of computational complexity ...
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Neural Networks and a catalogue of the number of floating point operations in various types of statistical and time series models

I recently came across this paper Green AI. In the paper they discussed using floating point operation (FPO) count during testing and implementation of Neural Networks (NNs) to compare the ...
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How to compute largest values of random variables? [closed]

Suppose we have two discrete random variables and we want perform maximum operation to obtain the max PDF. We know that max of two independent random variables is: if Z = max(X,Y) ...
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136 views

Time complexity of batch gradient descent

I am read http://papers.nips.cc/paper/4937-accelerating-stochastic-gradient-descent-using-predictive-variance-reduction.pdf paper. It states that "Due to the poor condition number, the standard batch ...
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knn asymptotic complexity vs svm [duplicate]

I'm doing a little report about the KNN complexity vs SVM.. I would like to know your opinions.. I built this text according to my perspective searching in papers, websites, ppts etc: The reason ...
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Who is more complex computationally knn or SVM? [closed]

I have trained two models using sklearn library in python.. My dataset was about 750 features, 250 features per class (three classes), I trained only one feature dimension (1-D array). This are the ...
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23 views

Time complexity for locality sensitive hashing similar image search

I am trying to find most visually similar images for large image dataset. (N=1 million), using LSH (Locality Sensitive Hashing). Image feature vectors are 4096 dimensional VGG-16 features. Now, my ...
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What are the time complexity of image feature extraction algorithms, including HS, HOG, MSER and SIFT?

Can somebody help me by writing me a time-complexity of each image feature extraction algorithms. Especially I am interested in Harris-Stephens(HS) corner detection, Maximally Stable Extremal Regions (...
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What is the computational cost of gradient descent vs linear regression?

I know the computational costs for the closed form of linear regression is $O(n^3)$, but I can't find a similar cost comparison to gradient descent. There are some similar questions here with people "...
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344 views

What does it mean for K mean problem to be NP hard and why?

Given a decision problem (a problem with yes or no answer), the problem is said to be NP-hard if there is an NP-complete problem Y, such that Y is reducible to X in polynomial time. Recall that NP-...
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182 views

How to inform the space and time complexity of K-means, SOM and Hierachical clustering

In the paper I am writing, one of the reviewers asked for an "a simple computational complexity analysis or time computational demands of their method" My question is : Can I simply report the ...
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241 views

K means clustering time fluctuates with increased value of K

I have written k means clustering code in c#. I am clustering random 99 text articles of Sports Area which I downloaded from Github for different values of K i.e.3,4,5,6,7. I want to analyze the time ...
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156 views

Computational complexity of sampling from discrete and continuous distributions?

What is the computational complexity of sampling from any of these cases? I mean the computational complexity of the most efficient existing algorithm, not a possible algorithm or a lower bound. ...
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Why does my LSTM take so much time to train?

I am trying to train a bidirectional LSTM to do a sequential text-tagging task (particularly, I want to do automatic punctuation). I use letters as the building-blocks: I represent each input letter ...
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148 views

Computational complexity of MaxiEnt classifier

I know that the time complexity of logistic regression can be as low as linear when the optimizer/solver is assumed to be linear, such as L-BFGS (this link) I know that multinomial logistic regression ...
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Clustering: Clique vs. Agglomerative with Complete-Link

In my data, I have a defined a symmetrical relation $R$ where $R(i,j)=R(j,i)$ indicates that $i$ and $j$ are closed each other. I need to find cliques $C_1,C_2,\dots,C_n$ where $C_k\cap C_l=\...
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What is the time complexity of spectral clustering and why is it so?

What is the time complexity of spectral clustering and why (mathematically speaking) is it so? What are possible existing alternatives to speed up the computations required by the algorithm?
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XGBoost paper - time complexity analysis

I'm reading through the XGBoost paper and I'm confused by the subsection of 4.1 titled "Time Complexity Analysis". Here the authors assert that the exact greedy algorithm with $K$ trees, a maximum ...
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137 views

What all does the training time for a neural network include?

I recently developed a DNN model and I want to know what exactly is training time and what all steps are included in it? For ex I carried out the following steps: Determined best Network ...
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GMM EM algorithm complexity per iteration

I was fitting GMM clusters with diagonal covariance on my data using EM with $n$ (=5e6) points, each having $m$ (=160) ...
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145 views

Dimension reduction methods: overview of complexity

For classical dimension reduction methods (PMF, PCA, SVD, t-SNE...) or some others, I need to know the complexity of efficient implementations: with $N$ vectors in dimension $d$ reduced to dimension ...
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156 views

Why is matrix notation in linear regression best way to compute coefficients?

I would to find the parameters for $y_i=\beta_0+\beta_1x_{1i}+\beta_2x_{2i}$ using the least squares concept and want to prove that matrix notation is computationally more convenient than my way below ...
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How can the xor function be formed with a single hidden layer of neural network?

I was recently viewing Andrew Ng's deep learning specialization lectures and I came forward to the following image It is pretty obvious how the above function( x1 XOR x2 XOR x3..... XOR xn) can be ...
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214 views

Where does the exponential time complexity in LDA's posterior of topics arise?

In Finding scientific topics (PNAS 2004) the authors derive the (marginalized) posterior distribution of topic assignments given the observed word and arrive at equation (4). Then, immediately after, ...
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126 views

Real using of the “Realized GARCH” for 1 minute forecast

I would like to ask someone who has an experience with the "Realized GARH" by Peter Hansen. I have 2 questions: Is there a logical purpose to use realGARCH for 1 minute forecast? How long could it ...
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465 views

Time complexity of the EM algorithm

this is Fuzzy Relational Eigenvector Centrality-based Clustering Algorithm (FRECCA). Here, N = total number of data, C is the number of clusters. Link of this algorithm is here For line 1-10, time ...
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995 views

Why are k-means and k-NN considered simple algorithms in machine learning?

We all know the k-means clustering algorithm and the k-nearest neighbors algorithm: the former is an unsupervised clustering method, and the latter is a supervised learning technique in machine ...
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278 views

Time Complexity Pooling Layers

What is the big oh complexity of Keras' GlobalMaxPooling1D() layer? More generally, how would you find the complexity of pooling layers?
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“Wrong polarity” of SVM in Bottou & Lin (2006)

I am reading the paper "Support Vector Machine Solvers" by Bottou and Lin (2006). On page 10, the authors engage in a discussion about the asymptotic number of support vectors as a function of the ...
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What is the time and space complexity of single linkage hierarchical clustering?

I have read everywhere that the time complexity of hierarchical agglomerative clustering is $\mathcal{O}(n^3)$ and it can be brought down to $\mathcal{O}(n^2 \log n)$. How do we arrive at such ...
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606 views

can the time complexity of k-nearest-neighbor allow it to be used as a clustering technique?

If I have N of about 3000 data points, each of about dimensions d of 50, and so the k in kNN is sqrt(3000/2) is about 40, then applying kNN to these points would be about O(NdK) = O(3000*50*40) which ...
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557 views

How does Lasso scale with the design matrix size?

If I have a design matrix $X\in\mathcal{R}^{n\times d}$, where $n$ is the number of observations of dimension $d$, what is the complexity of solving for $\hat{\beta}=\text{argmin}_{\beta}\frac{1}{2n} |...
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Supervised Machine learning classifiers big-O [closed]

I'm comparing different machine learning for classifying sensor data and I need their complexity to select the most efficient. Which are the Big-O notation for the following algorithms (I add what I ...
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113 views

What is the feasibility to run linear model for large amount of data?

I am looking for empirical approximations and guidelines on how many operations are required to run a linear model on a given amount of data, or if it's even feasible. Let's assume we use QR ...
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How to derive the time computational complexity of k-medoids (PAM) clustering algorithm?

I have read that the time complexity of k-medoids/Partitioning Around Medoids (PAM) is O(k(n-k)^2). I am trying to understand how this algorithms translates into this time complexity. As per my ...
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The relation of time-series signals complexity and other statistical and signals processing concepts

What is the relation between correlation and time-series signal complexity? For example, I was reading a paper that is talking about the Multi scale entropy (MSE) and its advantages over the Shannon ...
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189 views

What are the computational complexities of Linear One-vs-One, Bayesian Multivariate, and k-NN algorithms?

What are the computational complexities of Linear One-vs-One Committe, Bayesian multivariate with the class independence assumption, and k-NN algorithm with k=3? In $\mathcal{O}$ (Big-O) notation?...
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Algorithmic Complexity of Estimators

I am interested in evaluating the algorithmic complexity of an estimator of the form: $$\hat{\theta} = \text{argmin}_{\theta} \;\; Q_n (\theta)$$ where $Q_n(\theta)$ denotes some objective function ...
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486 views

How can one estimate compute requirements for Machine Learning algorithms?

Has anyone developed formulas or rules of thumb for estimating CPU, memory and time requirements for running various Machine Learning algorithms (or families of algorithms), with respect to training ...
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112 views

Effect of training data on complexity of kernel

How does the amount of training data affect the complexity of a linear kernel in support vector machine?
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28 views

weighing of probabilities in a multi horizon framework

I shall start with an example so it's clear what I'd like to explore: I have to decide how many sigarettes to smoke in a day. One person tells me they will me kill should it rain. his credibility ...
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2k views

Complexity of a random forest with respect to maximum depth

I expect the training time of a random forest to be : linear in the number of trees (obviously), linear (or square-root) in the number of columns (depending on the choice for the subsampling of the ...
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k-NN computational complexity

What is the time complexity of the k-NN algorithm with naive search approach (no k-d tree or similars)? I am interested in its time complexity considering also the hyperparameter k. I have found ...
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667 views

Computational complexity of the lasso (lars vs coordinate descent)

The lasso can be computed with the LARS or Coordinate Descent algorithm. What is their computational complexity and when one is quicker than the other?
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Reference summarizing various machine learning algorithms' computational complexity

For example, suppose you train a linear regression model using the Normal Equation, on a training set $\mathbf{X}$ containing $m$ instances and $n$ features. The Normal Equation requires computing $(\...
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How to determine time complexity of EM algorithm of probabilistic PCA?

I was studying probabilistic PCA from Bishop's book. There an EM algorithm is provided to calculate principal subspace: Here $\mathbf M$ is $M\times M$ matrix, $\mathbf W$ is $D\times M$ matrix and $...