Questions tagged [sparse]

A sparse matrix is a matrix where many of the elements are zeros. The tag can also be used for sparsity in other contexts, such as regression models with sparsity, or the "bet on sparsity"-principle.

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Correaltion between sparse variables

I have an Events x People matrix M, where a cell (e,p) gives the score of person j at event e. Let E be the total number of events. Each person has attended a lot of events, say 0.3*E at an average. ...
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31 views

How is explained variance in sparse PCA calculated?

Sparse PCA is a technique proposed by Zou et all in this paper. In usual PCA the obtained loadings are orthonormal, and the resulting scores are uncorrelated. However, in sparse PCA you give up these ...
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17 views

Using Pearson correlation coefficient in sparse data

I have been using the cor function in R to compare correlation between my variables. The data did pretty poorly with 2/3 of them having a correlation close to 1 with some other variable. However the ...
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160 views

What does Sparse PCA implementation in Python do?

I am interested on using sparse PCA in python and I found the sklearn implementation. However, I think this python implementation solves a different problem than the original sparse pca algorithm ...
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19 views

How does Data Augmentation work for supervised learning models?

I've ran into a few Kaggle competitions where the winning solution used data augmentation, and a new ML platform, which claimed to help with Data Augmentation. Use cases were imbalanced classes and ...
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30 views

Computation of generalized least squares solutions of large sparse systems

Suppose $X$ and $\Omega$ are large sparse matrices, with $\Omega$ symmetric positive definite (but not diagonal), and $y$ is a vector. I want to find the generalized least squares solution: $$\hat\...
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7 views

method for determing the important factor for high dimension categorical data

I have around 1000 people with total 400 categorical features, but each one will only have subset of those 400 features(ranging from 3-60 for this population), thus the dataset is fairly sparse. Now I ...
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496 views

Shrinkage priors

I am building a Bayesian model where I to put shrinkage priors such as spike and slab, horseshoe prior, etc on some parameters for feature selection, but I am not able to decide which one is the best. ...
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109 views

What are the benefits of sparse representations and sparse parameters?

What are their benefits? I know sparse parameters are a different story than sparse representations, but I want to know how each of these can benefit us and which one is more important than the other ...
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20 views

How to get adjusted explained variance of PC using Sparse PCA in R

I am using "elasticnet" package to do the sparse PCA. However I could only get the percent of explained variance of each PC. I am wondering can I get the adjusted explained variance of each PC using "...
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41 views

Extracting the right summary statistics from zero-inflated data sets (i.e. a sparse matrix where everything non-zero is a statistical outlier)

I'm a consumer tech startup founder with rudimentary background in statistics. I need help in processing a large, sparse matrix. I'm logging all actions users are undertaking in my app. I then ...
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30 views

Comparing clusterings of different spaces

I have developed a graph embedding method that learns feature representations for each node in the graph based on the graph topology. I want to demonstrate that the learned feature vectors yield ...
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26 views

How to interpret the learning curve of a LinearRegression for sparse data?

I have a dataset of shape ca.(4800, 350). Both the dataset X as well as the response y is very sparse (ca. 3500 samples with y=0). I wanted to take a look at the learning curve to estimate the bias-...
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99 views

Sparse linear poorly constrained least-squares problem

I have a somewhat simple linear problem. I have data $D$ (a vector with a few million elements), the parameter vector $X$ (a couple of thousands elements) and the design matrix $A$ which is extremely ...
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74 views

Combining many sparse binary variables

Based on kjetil b halvorsen suggestion, I rephrased my problem: My problem is analogous to the following: i am supposed to predict if a high school student will go to university (Yes/No). I have ...
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28 views

Nonlinear approximation of a sparse linear transformation

Suppose that we have $y = Ax$ where $x$ is a vector of size $m \times 1$, $A$ is a sparse matrix with size $n \times m$. Suppose that $n \times m$ is very large and we wish to find a non-linear ...
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34 views

How to build a machine learning model from sparse features with class imbalance?

I have around 10 numerical features and 1 class/target (e.g., visitors count of a website). All of them are sparse. Sparsity is around %70-80. The median of the class/target is zero. Is there a good ...
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8 views

Appropriate machine learning technique for spectral data and low-frequency feedback

I have a performance measure and a data source that basically supplies a complex and varying waveform. I would like to apply some unstructured learning technique to try and find a pattern in the ...
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128 views

Clustering Binary and Continuous Features

If you need to cluster a dataset with the following characteristics: It has a mix of binary and continuous features. It is very sparse. For most features, you only have values for 15% of the ...
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27 views

Why neural network does not learn sparse relationship [duplicate]

The universal approximation theorem says that a neural network can be used to approximate any continuous function under some regular conditions with arbitrarily small approximation error, provided we ...
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Probability of sparse spectrum

Consider a vector $v$ such that $v \sim \mathrm{Unif}(\mathbb{S}^{d-1})$, the uniform distribution on the unit sphere in $d$ dimensions. Question: is there an upper bound on the probability that $v$ ...
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Is it useful to use sparse regression (e.g. Lasso) when the number of observations is significantly larger than the number of covariates?

I'm learning about penalized/sparse regression and I noticed that the examples used for penalized/sparse regression, e.g. Lasso, are usually cases where the number of observations is significantly ...
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69 views

How to conduct a principal component analysis on data set with large number of zeros

I have data for percentage cover of plant species in 500 sites. There are columns for 30 different species in the data set and I would like to drastically reduce this down to a manageable number of ...
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26 views

Notation problem with sparse regularized correlation matrix

I am trying to apply a specific method to obtain a sparse correlation matrix $R$ from a regularized correlation matrix $\Sigma^{\delta}$, which was computed from $N$ observations of a multivariate ...
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9 views

Regress in two variables against basis functions when one of them might be “sparse”

I'm tasked with the problem of fitting a series of functional forms $\{f_t(S,K)\}$ along the time axis. At each time $t=0,1,\cdots,T$, there are $N_t$ samples $$(F_{t,i}, S_{t,i}, K_{t,i}),\quad i=1,2,...
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60 views

Efficient way to do Autoencoder on large sparse matrix

I have a large csr_matrix of shape (60,000, 180,000) and about 99.7% sparsity. I was trying to train an autoencoder for this matrix via mini-batch optimization. I tried batch size of 6000 with ...
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20 views

Relationship Between PCA Principal Components & Dictionary Learning Atoms

Suppose I am given an image, where I generate n random 16x16 patches that are each flattened as 256 x 1 vectors, i.e. the number of variables p is 256. Upon performing PCA, I find $min(n, p)$ ...
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32 views

estimate sparse localized whitening transformation

This is a follow-up to estimate precision matrix with given spatial sparsity pattern, expanding on the second part of that question and formulating more precisely using material from the answer by ...
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119 views

Does anyone know the rank of the Netflix Prize dataset?

I'm looking into the Netflix Prize at the moment. We model the dataset as an $n \times m$ matrix, where $n$ is the number of users and $m$ is the number of movies. Does anyone know the rank of the ...
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393 views

Autoencoder for sparse data

Suppose I have a big (1,000x20,000) sparse (95% of elements are zeros) matrix with counts. I want to use autoencoder to encode-decode this matrix. How should I do it? Are there any tricks or ...
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150 views

estimate precision matrix with given spatial sparsity pattern

I have a set of $n$ measurements of $p$ variables $\xi_i$. I am interested in the inverse covariance or precision matrix $P$ of the variables, but because $p \gg n$ and because of limited storage ($p$ ...
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210 views

LSTM time series forecasting on sparse dataset

I am working on the LSTM time series forecasting of solar energy production. The available data is one year on a half hourly basis. More than 60% of the data values are zero as the PV stations cannot ...
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39 views

Longitudinal study - generalised linear mixed model - dealing with very wide confidence intervals due to sparsity in the outcome

I am conducting a treatment evaluation using administrative data. It is a population-based study of all people diagnosed with a specific disorder in two calendar years (N = 2300). I have run a GLMM ...
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21 views

How much data is considered “sparse” for fitting a mixed (Beta Geometric) distribution with 4 shape parameters?

I'm using CamDavidsonPhillips Customer Lifetime Value library to calculate CLV, and it uses a distribution based on Peter Fader's work on the subject that fits a Gamma distribution to model customer ...
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108 views

Literature on $\ell_q$ LASSO, $q < 1$

I am not sure how is $\ell_q$-LASSO called, but here I am talking about LASSO regression, with $\| \beta \|_{\ell_q}$ regularization, $q< 1$. In popular literature, such as Elements of Statistical ...
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16 views

How to develop features for deep learning from cart items data?

I wonder how to approach building set of features to feed deep learning model (eg convnet) from cart items data: 5pcs of product1 1pcs of product5 2pcs of product8 Assuming 30-50 products per ...
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34 views

Is low rank finite-iteration manifold identification possible?

In sparse optimization, I am trying to solve the problem $$ \min_{x\in \mathbb R^{n}} \quad f(x) + \|x\|_1 $$ and at optimality, $x^*$ may be sparse. If I define the sparse manifold as $\mathcal M = ...
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39 views

finding sparse regions in time series data

I have several hundred years of church baptisms that will be searched by people wanting to find the baptisms of their ancestors. I want to call attention to periods in the records in which the number ...
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1answer
3k views

Do you standardize the data before PCA whitening?

I have a data set ranged in different scales as well as some variables are sparse, for example, ...
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89 views

Normalizing sparse matrix by mean, should the mean be calculated excluding zero?

I have very sparse matrix (70% sparsity) which I want to normalize by mean. I tried using mean both include and exclude zero. The histogram between count (y-axis) and value (x-axis) shows The value ...
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225 views

GAN and NN for sparse data

I have a set of images which represent some correlated sparse data $x_1,\ldots ,x_n$. there are a number of specific pixels in the images which might hold value or not (with some probability), while ...
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1answer
244 views

Simulation of low rank and sparse matrix

I am having trouble simulating a matrix which is low rank and sparse (sparse along both rows and columns). One way to simulate a low-rank matrix is by generating a random matrix, then taking SVD and ...
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2k views

Can it be over fitting when validation loss and validation accuracy is both increasing?

Training a simple neural network over a very sparse matrix (Has 2400 features and 18000 train rows) for a binary classification problem. At the end of 1st epoch validation loss started to increase, ...
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236 views

Amount and sparsity of data for recommender systems

I'm starting to work in a project that will have a recommender system as one of its components. I'm trying to figure out if I have the right type of data for the recommender. The data contains ...
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70 views

Confidence region for multinomial distribution with k=7 - including 5 zero values in dataset

I have a multinomial distribution with $k=7$ and an observed dataset $n_i = \{62, 35, 0, 0, 0, 0, 0\}$. While it was quite expected that $n_i = 0$ for $i \in \{3,4,...,7\}$, there was no way to ...
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39 views

How to prove oracle properties in Fan and Li (2001) paper

I am studying Fan and Li's 2001 paper "Variable selection via nonconcave penalized Likelihood andits oracle properties" but I am having troubles understanding Theorem 1 proof (page 1359). I follow the ...
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329 views

Data sparsity becomes a problem

I read this in a paper Developing an approach toward virtual synthesis parameter screening introduces two primary computational challenges: data sparsity and data scarcity. ...Such canonical ...
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17 views

Question about minimax risk sparse sparse condition

I am studying statistical leaning theory. Especially the paper "Minimax rates of Estimation for High Dimensional Linear regression over $l_q$ balls" by Garvesh Raskutti .et.al. In the right end of ...
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Is max. Eigenvalue of k-sparse PCA always $\leq$ max. Eigenvalue of normal PCA on same dataset?

Is max. Eigenvalue of k-sparse PCA always less than or equal to the max. Eigenvalue of normal PCA on same dataset? K refers to the number of non zero eigenvalues when the dataset is of dimension n <...
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2k views

How to do dimension reduction with sparse data

I have 200 vectors representing the percentage marks for 200 different students in the different classes they took. The vectors are 22 dimensional (as there were 22 different classes in total) even ...