biglasso extends lasso and elastic-net linear and logistic regression models for ultrahigh-dimensional, multi-gigabyte data sets that cannot be loaded into memory. It utilizes memory-mapped files to store the massive data on the disk and only read those into memory whenever necessary during model fitting. Moreover, some advanced feature screening rules are proposed and implemented to accelerate the model fitting. As a result, this package is much more memory- and computation-efficient and highly scalable as compared to existing lasso-fitting packages such as glmnet and ncvreg. Bechmarking experiments using both simulated and real data sets show that
biglasso is not only 1.5x to 4x times faster than existing packages, but also at least 2x more memory-efficient. More importantly, to the best of our knowledge,
biglasso is the first R package that enables users to fit lasso models with data sets that are larger than available RAM, thus allowing for powerful big data analysis on an ordinary laptop.
biglassoat least 2x more memory-efficient than
ncvreg (3.12-0), and
lambdavalues equally spaced on the log scale of
lambda / lambda_maxfrom 0.1 to 1; varying number of observations
nand number of features
p; 20 replications, the mean computing time (in seconds) are reported.
y = X * beta + 0.1 eps, where
epsare i.i.d. sampled from
biglassois more computation-efficient:
In all the settings,
biglasso (1 core) is uniformly faster than
ncvreg. When the data gets bigger,
biglasso achieves 6-9x speed-up compared to other packages. Moreover, the computing time of
biglasso can be further reduced by half via parallel-computation of multiple cores.
biglassois more memory-efficient:
To prove that
biglasso is much more memory-efficient, we simulate a
1000 X 100000 large feature matrix. The raw data is 0.75 GB. We used Syrupy to measure the memory used in RAM (i.e. the resident set size, RSS) every 1 second during lasso model fitting by each of the packages.
The maximum RSS (in GB) used by a single fit and 10-fold cross validation is reported in the Table below. In the single fit case,
biglasso consumes 0.60 GB memory in RAM, 23% of that used by
glmnet and 24% of that used by
ncvreg. Note that the memory consumed by
ncvreg are respectively 3.4x and 3.3x larger than the size of the raw data.
biglasso also requires less additional memory to perform cross-validation, compared other packages. For serial 10-fold cross-validation,
biglasso requires just 31% of the memory used by
glmnet and 11% of that used by
ncvreg, making it 3.2x and 9.4x more memory-efficient compared to these two, respectively.
Note: ..* the memory savings offered by
biglasso would be even more significant if cross-validation were conducted in parallel. However, measuring memory usage across parallel processes is not straightforward and not implemented in
Syrupy; ..* cross-validation is not implemented in
picasso at this point.
The performance of the packages are also tested using diverse real data sets: * Breast cancer gene expression data (GENE); * MNIST handwritten image data (MNIST); * Cardiac fibrosis genome-wide association study data (GWAS); * Subset of New York Times bag-of-words data (NYT).
The following table summarizes the mean (SE) computing time (in seconds) of solving the lasso along the entire path of 100
lambda values equally spaced on the log scale of
lambda / lambda_max from 0.1 to 1 over 20 replications.
|picasso||0.67 (0.02)||2.94 (0.01)||14.96 (0.01)||15.91 (0.16)|
|ncvreg||0.87 (0.01)||4.22 (0.00)||19.78 (0.01)||25.59 (0.12)|
|glmnet||0.74 (0.01)||3.82 (0.01)||16.19 (0.01)||24.94 (0.16)|
|biglasso||0.31 (0.01)||0.61 (0.02)||4.82 (0.01)||5.91 (0.78)|
To demonstrate the out-of-core computing capability of
biglasso, a 96 GB real data set from a large-scale genome-wide association study is analyzed. The dimensionality of the design matrix is:
n = 973, p = 11,830,470. Note that the size of data is 3x larger than the installed 32 GB of RAM.
Since other three packages cannot handle this data-larger-than-RAM case, we compare the performance of screening rules
Adaptive based on our package
biglasso. In addition, two cases in terms of
lambda_min are considered: (1)
lam_min = 0.1 lam_max; and (2)
lam_min = 0.5 lam_max, as in practice there is typically less interest in lower values of
lambdafor very high-dimensional data such as this case. Again the entire solution path with 100
lambda values is obtained. The table below summarizes the overall computing time (in minutes) by screening rule
SSR (which is what other three packages are using) and our new rule
Adaptive. (No replication is conducted.)
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