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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Loss of captured variance in sPCA

Good morning to all I am trying to run the Sparse Principal Component on a synthetic dataset I created. I noticed that the captured variance does not reach 100% (cumulative proportion), but on the ...
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Recommendation for books about statistical data analysis with sparse data ( a lot of zeros)

Evident from the title, i am looking for books about the general statistical data analysis techniques such as hypothesis testing, etc but for large and sparse dataset.
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How to choose tuning parameters for SparsePCA

Good morning to everyone. I'm studying the paper "Sparse Principal Component Analysis Hui ZOU, Trevor HASTIE, and Robert TIBSHIRANI" (Link: https://hastie.su.domains/Papers/spc_jcgs.pdf) At ...
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Obtain principal components from the loading vectors

Good morning, everyone. I am trying to use the "SparsePCA()" function of Matlab whose documentation link is below available. https://www.ml.uni-saarland.de/code/sparsePCA/sparsePCA.html This ...
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Creating a random sparse precision matrix?

In my current project, I want to create a random sparse precision matrix $\boldsymbol{P}=\boldsymbol{\Sigma}^{-1}$ (the inverse of a covariance matrix $\boldsymbol{\Sigma}$). My current procedure ...
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How do Sparsity Priors help for Identifiability?

Let's say we have a Factor Analysis model with a latent variable $\mathbf{z}_t \in \mathbb{R}^k$: $$x_t = A z_t + \epsilon_t, \qquad \epsilon_t \sim \mathcal{N}(0, \Sigma)$$ Let $A \in \mathbb{R}^{g\...
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Questions about the exact covariance - matrix and Adjusted Total Variance

Good evening everyone. Regarding the topic related to Sparse PCA. For example, in "Sparse Principal Component Analysis Hui ZOU, Trevor HASTIE, and Robert TIBSHIRANI" the authors mention the ...
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Features differ between classes

Good evening everyone. Regarding the topic related to Sparse Clustering (for example K-Means). For example, in "Witten DM, Tibshirani R. A framework for feature selection in clustering" the ...
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Does dataset sparsity affect rate of convergence of model solution?

I have a model with not too many ordinal data. The model performs at a 90% accuracy. I am thinking of adding 13 ordinal variables and transforming them using one hot encoder. The transformation will ...
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How to implement simple VAE with sparse tensor in Tensorflow

thank you for reading. I have been attempting to train a simple VAE on very sparse 2D and 3D data. So far I have been training using dense tensors which - I think - is resulting in horrible training ...
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Multivariate time-series with asyncronous data

I have quote observations for 9 FX rates, which I would like to analyze via multivariate dynamic linear model (e.g., Chapter 16 in West and Harrison Bayesian Forecasting and Dynamic Models (1997). In ...
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Does 'sparse' mean different in sparse feature & sparse representation?

In Google developers site, the meaning of the word sparse seems to contradict between the following two definitions: sparse feature: Feature vector whose values are predominately zero or empty... ...
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Car rental time series forecasting

I have the time series of car rentals/demand in a location. The time axis is every hour for 3 months. The y-axis is number of car rentals/demand. I want to do prediction for future hours given this ...
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Item clustering to help with extremely sparse collaborative filtering

I have a large collaborative filtering dataset, where items are images. Some have text, other don't, some are quite visually similar. I do know that some items are similar, e.g. I have 10 distinct ...
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How to use sparse PCA loadings in a regression?

I'm using Dr Frank Harrell's code in RMS 2nd edition. He goes into sparse PCA. Does anyone know how to code a regression model after getting the sparse component grid? ...
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Fitting Sparsed Constrained regression with non-negative coefficients adding to 1

I see a similar problem in How do I fit a constrained regression in R so that coefficients total = 1? Specifically, my model is $Y_i= \pi_1 X_1+\pi_2 X_2 +...+ \pi_K X_K +\epsilon_i$ with $\pi_k \ge 0$...
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T-testing on sparse data

Problem: I have two stochastic processes, $S_1$ and $S_2$, that frequently are zero, but occasionally have positive values with unknown probabilities $q_1$ and $q_2$. e.g. $$ S_1 = \{0,0,0,0,0,21,0,0,...
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Why lasso cannot be arbitrarily applied?

Consider any log likelihood function $f(\theta|x)$ where $x$ is data. I can consider $f(\theta|x)+\lambda||\theta||_1$ where $||\theta||_1$ is the standard $L_1$ norm. It seems that I cannot apply ...
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How to solve the problem of having sparse data that would become too small when aggregated?

I have a dataset that provides the count of cyber incidents since 2011 for different countries and different attack types, and I want to use this data in a machine learning model to predict future ...
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Is it wrong to run a Random Forest on high-dimensional, sparse, and unbalanced data?

I am learning about random forests, and I have been testing using R. I have doubts about whether I am doing something wrong given that my data are: sparse, high-dimensional, and unbalanced. Trying to ...
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Working with sparse data in numpy and sklearn [closed]

I have a time series dataset geenrated from some electrophysiological data. I have a frequncy dataset and the matrix is quite sparse but huge, like it contains 0.005 s time bins for 2000+ neurons ...
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bootstrapped l2,1 least square does not produce sparse solution

I am trying to model an autoregressive model with $\ell$-2,1 regularization, where $\|X\|_{2,1}=\sum_i|\sum_jX_{ij}|$: $$y_{t+1} = wx_{t} + \lambda_1\|w\|_{2,1}, y\in \mathbb{R}^{n_1}, x\in \mathbb{R}^...
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Variable selection with sparse data

I have a dataset with 141 observations and 8 corresponding variables and I mean to apply a GLM to this dataset. However, a lot of observations lack either one or multiple variable values. So if I want ...
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What is the degree of cell sparsity that Poisson model can tolerate?

For models with no interaction terms, my understanding is that all the marginal cells need to have non-zero counts, in order to have finite estimates. If this minimum requirement is satisfied, will a ...
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How to compare row entries in a sparse table with lots of missing values?

I have a dataset with ~1000 laptops and performance results across ~100 different benchmarks. Using the benchmark results, I want to give each laptop a single composite performance score, and rank the ...
4 votes
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Autoencoder doesn't learn 'sparse' input images

I am trying to train an autoencoder with PyTorch on 2D images containing 2D Gaussian densities such as this: The images are of size 100x100 (I feed them into the autoencoder as 1x10000 tensors). The ...
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What is the difference between network sparsification and model pruning

What is the difference between network sparsification and model pruning? I watched USENIX ATC '21 - Octo: INT8 Training with Loss-aware Compensation and Backward Quantization for Tiny (at 01:29sec) ...
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What are the references for different active set selection methods for sparse Gaussian processes?

I am comparing the different sparse Gaussian process approaches within the fitrgp function in Matlab, but I am struggling to find references for the different choices within the function for the ...
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Fit a histogram of sparse data with a monotonically decreasing function

I have a business problem where essentially we have counts across a certain metric which at times suffer from low observation counts! So essentially when you look across the bins you'll have adequate ...
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Compatibility condition in LASSO

I am reading Statistics for High-Dimensional Data (Bühlmann and van de Geer). Chapter 6 discusses obtaining the oracle inequality in LASSO under the compatibility condition, a technical assumption ...
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Oracle inequality for LASSO

In chapter 6 of Statistics for High Dimensional Data (Peter BühlmannSara van de Geer), they focus on the normal linear regression model with fixed regressors and begin by stating OLS achieves a risk $\...
2 votes
1 answer
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Bayes prior in MAP estimation corresponding to $\ell^0$ penalization

I gather that in the context of penalized least squares, we can interpret a penalty term as corresponding to a prior $\pi(\beta)\propto \exp\{-\text{pen}\}.$ Is this also true for $\ell^0$ ...
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Bayesian priors associated with regularization penalties

I gather that adding a penalty term to (linear) least squares minimization typically corresponds with choosing some prior for Bayes estimation in the normal linear regression model. A couple questions ...
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LASSO with $L_p$ norms for $1 < p < 2$?

For the sparse linear regression problem, minimizing the LASSO objective $\| X \beta - Y \|_2^2 + \lambda \| \beta \|_1$ is known to recover the optimal data generating parameter $\beta^*$ with the ...
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regarding the loss function for the sparse autoencoder

I am implementing a sparse autoencoder using dictionary learning framework, i.e. instead of using a neural network in Keras, Pytorch or Tensorflow, I am using only matrices to represent the different ...
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Doubts about generating a synthetic dataset according to a paper

I'm trying to replicate the experiment reported in section 3.3 of this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2930825/) but I'm struggling to understand how the synthetic dataset is ...
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Do we need to shrink bias term in a sparse linear model?

In a sparse linear model, we put shrinking constraint on parameters associated with predictors only as the following optimization problem: $minimize_{\omega_0, \omega} (1/2n (\|y-\omega_0 \textbf{1} - ...
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binary one dimensional k-svd

I have a problem that is somehow between k-means and k-svd: I would like to find a vector $D=[d_1, d_2, d_3..., d_k]$, so that the elements of another vector $Y=[y_1,y_2,y_3..., y_n]$ with $k \ll n$ ...
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If there is a sparse solution then is the smallest l1 norm solution at least as sparse?

Consider the linear equation $Ax=b$ where $A$ is a matrix and $b$ and $x$ are vectors. Suppose there exists a vector $x_S$ that solves this equation ($Ax_S=b$) and $x_S$ has $k$ entries of value $0$ (...
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Multiple regression with sparse X

I would like to run the multiple regression: $$y = X \beta + \epsilon \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)$$ with: $n \sim 2 \times 10^6$ $p \sim 10^4$ $X$ sparse 70% of rows have 1 non-...
2 votes
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In a sparse reward problem, is it possible to remove reward shaping once the RL agent trains long enough to consistently reach the final reward?

I'm new to machine learning, and primarily looking at it from the perspective of it's applications to control theory. In the application found in this paper, a RL agent attempts to land a spacecraft ...
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LARS package in R with specific lambda value

I am trying to use the LARS package in R to obtain a Lasso estimate of the sparse coefficient vector, say $\hat{\beta}_{\text{sparse}}$, as opposed to a coefficient path. In other words, I am not ...
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outlier detection for sparse data in categorical variable

I have a big dataset with a column "clientid" and a categorical column "choice". I want to find out what are the clients that have strange combinations of choices (less frequent ...
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55 views

Calculate Data Sparsity - There are no 'zeros'

I am being asked to provide the percentage of data sparsity in my dataset. The challenge I am running into is that there isn't traditional sparsity in my data, no 'zeros', 'NAs', '-' etc.. I am ...
3 votes
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280 views

Clustering text embeddings: TF-IDF + BERT Sentence Embeddings

I am trying to cluster a few thousand forum posts that are similar in content to Stackoverfow. So far, I have tried two main approaches to represent the posts: TF-IDF Sentence embedding based on BERT....
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Scaling a sparse matrix

I want to apply sparse PCA to a sparse matrix. I was wondering if scaling to mean 0 and unit variance would be appropriate given that my input is sparse?
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Probability distribution associated with nuclear norm?

The $\ell_1$ norm of model parameters is often added to loss functions because it induces sparsity in the solution of the overall cost function: $$ c(\theta) = -\log L(x|\theta) + \lambda ||\theta||_1$...
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Are Spiking Neural Networks The Next Big Thing? [closed]

Intel recently announced their Loihi chip as part of their "Neuromorphic Computing" research, which is optimized for spiking neural networks (SNNs). I found an example of a problem in which ...
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Reconstruction metric robust to scaling, sparsity, and outliers?

I seek a reconstruction error metric with following properties: Robustness to sparsity: error decreases in presence of many zeros or small values (if predicted correctly) Scale invariance: error ...
1 vote
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unsupervised anomaly detection on sparse data

Given that I have a very sparse data matrix with continuous features, like this dataframe for example ...

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