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Questions tagged [penalized]

Methods of modifying objective functions to control the solutions of optimization problems.

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8 views

In case of elastic-net regression, what is the updating equation of gamma0

In case of elastic-net regression, what is the updating equation of gamma0 I have a proble with dealing elastic-net regression for gamma and beta, ( argmin 1/2nSummation(yi-gamma-bxi)^2 + lambda(1-...
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17 views

Link between norm of weights/coefficients and smoothness

We often avoid overfitting by penalizing the norm of the weights/coefficients (in a classic Ridge or Lasso regression). I understand that we want smooth functions as they will be more likely to ...
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1answer
60 views

Why doesn't penalized cubic regression reduce the number of knots in a GAM?

As far as I understand, cubic regression penalization prevents overfitting by reducing the number of knots by penalizing wiggliness. The supplied parameter k serves ...
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59 views

LASSO regression: which method is better for selecting $\lambda$ in this case?

I am currently working on a method for adaptive knot placement in Spline regression. Following Osborne et.al. (1998), Yuan et.al. (2014) I am interested in using LASSO regression to select a subset of ...
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29 views

Selection criteria for penalty parameters in the ridge multinomial logit model

I appeal to you for the following doubt. I am adjusting a ridge multinomial logit model but I have problems in the criterion when choosing the lambda parameter that gives better results, besides ...
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1answer
92 views

A reward becomes a penalty if

I am working to build a reinforcement agent with DQN. The agent would be able to place buy and sell orders for a day trading purpose. I am facing a little problem with that project. The question is "...
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1answer
48 views

why does lasso select at most n predictors?

From the seminal paper on elastic net regularization from Zou and Hastie 2005, I read ...
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14 views

Multinomial logit with ridge penalization and value of time

I am fitting a multinomial logit model with ridge penalty and in turn estimating the value of time (VOT) or availability to pay (WTP). I want to work with real and simulated data. For the real data I ...
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11 views

Penalized regressions with forecast package and ets in R

Is there a way within the forecast package and ets to remap or penalize residuals based on some user defined function? E.g. If one wanted to impose a skew in error minimization, is this possible? ...
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44 views

Finding the “optimal” non linear relationship between two variables

I am looking for finding associations between a binary outcome regarding women fertility and several potential risk factors. Since this study is quite exploratory, I was planning to include all my ...
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46 views

Removing the intercept term for penalized logistic regression

I am working on lasso logistic regression and am trying to remove the intercept term from the penalty function. I have tried to use the mean centering theory but for logistic regression it can not be ...
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1answer
62 views

Large value of $X\beta$ in logistic regression?

In logistic regression, the probability is obtained from $$ Pr = \frac{\exp(X\beta)}{1 + \exp(X\beta)} ~~~~ (1) $$ From the plot below, it is obvious that if $X\beta$ > 10, the probability approaches ...
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1answer
61 views

Confidence limits for constrained penalized log likelihood model

I am estimating parameter $\beta$ as: \begin{align} \hat \beta &= \mathop{\mathrm{arg\,max}}_\beta \;\; l(\beta;X,y) - \frac{\lambda}{2}\left(\tilde y-g(\beta,\tilde X)\right)^\prime C^\prime C\...
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50 views

Adding additional constrains to OpenAi Gym

I'm currently working trough some examples which should finally end in a DQN Reinforcement Learning for the CartPole example in the openAI-Gym. Copied some code from GitHub which isn't deep yet: <...
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160 views

Calibration of penalized (LASSO or ELasticNet) logistic regression models

I would be very grateful for any help me with the following general query regarding calibration of penalized models with a binary outcome. I would like my prediction model to be calibrated (mean ...
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69 views

Elastic Net and collinearity

I am performing elastic net for variable selection on a dataset of 95 records and 41 variables. The response is a continuous numerical. I choose the alpha and lambda parameters through 10 fold cross ...
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1answer
156 views

Elastic net visualization [closed]

Sorry for the naive question, but is there a way to display in a graph the elastic net (or penalized regression in general) results? Specifically, how can I render the coefficients of the variables?
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1answer
458 views

Does Regularized Logistic Regression Produce Calibrated Results?

It has been asked and addressed here that logistic regression modelling is calibrated already and there is no need for calibration of it. To me it seems the argument provided there does not follow ...
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1answer
172 views

Sample size calculation for elastic net regression

I am using elastic net regression to investigate the effect of preditors on the response variable while accounting for multicollinearity among the predictors. But I wish to perform a sample size ...
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0answers
19 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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1answer
224 views

Interpreting glmnet Lasso coefficients on dummy variables (multiple levels) [duplicate]

I am trying to apply glmnet's lasso to a set of features in which there are multiple categorical variables with multiple levels. My intention is to let lasso reduce ...
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57 views

Using covariates from penalized regression model in unpenalized model

The good news where I am is that researchers are doing less stepwise covariate selection now that I've introduced penalized regression. The bad news is that researchers want to use elastic-net ...
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72 views

In LASSO, does it make sense to choose lambda based on the mean error associated with different lambda values, over multiple cross-validations?

I am running a LASSO regression, but am put off by the different values of lambda each time I run the cross-validation. Does it make sense to run a cross validation multiple times, take the mean error ...
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1answer
884 views

Why is R Squared not a good measure for regressions fit using LASSO?

I have read in several places that R Squared is not an ideal measure when a model is fit using LASSO. However, I'm not clear on exactly why that is. In addition, could you recommend the best ...
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23 views

Combining multiple imputation with penalization

I have used Frank Harrell's excellent rms package both for penalization (pentrace and setting ...
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0answers
103 views

Equivalent of using a Poisson prior in terms of a penalized regression?

I know that most penalized regressions have also a Bayesian interpretation, e.g. ridge least squares regression corresponds to the MAP estimate obtained under a Gaussian prior in a Bayesian regression,...
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115 views

How do you explain many optimal models in penalized Logistic regression?

I am building penalized logistic regression using Lasso and Ridge methods. I know that the best model chosen by the program is which has alpha = 1 and lambda = 0.06....
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55 views

“beta_given” column in the h2o.glm beta_constraints

What does the "beta_given" column do in the h2o.glm beta_constraints parameter? h2o is an open source library for machine learning algorithms. There are several online examples on how to install the ...
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236 views

Minimum number of observations for Lasso, LassoCV, LassoLarsCV

I have monthly fund returns for 3 years i.e. 36 observations (in some cases I may have 2 years i.e. 24 observations as well), and there are ~50 predictor variables. Both the dependent and independent ...
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25 views

Comparing shrunk model vs null model?

I have a null model $M_0$ with parameter $\theta$ and a more general model $M_1$ with parameters $(\theta,\alpha)$. I know that $M_0=M_1$ for $\alpha=0$. I am estimating $M_1$ using a penalized ...
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1answer
277 views

How is the minimum $\lambda$ computed in group LASSO?

The LASSO problem works by minimizing $$\min_\beta (\frac{1}{2}\left\rVert y-X\beta\right\rVert^2_2+\lambda\left\rVert\beta\right\rVert_1)$$ Here in this webpage I found that the minimal value of ...
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0answers
15 views

Elastic net with increased penalty for lower quality features

I’m building multinomial classification models using features characterized with high false-positive rate. Meaning, as the signal rate of the feature is lower (say gene expression abundance) the more ...
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1answer
107 views

How to find smallest $\lambda$ such all lasso coefficients are set to 0, depending on the intercept?

While bouilding a LASSO-penalized model it is well known that $\lambda =\left\lVert X^ty\right\lVert_\infty$ is the minimum value for which all the $\beta$ coefficients of the model are 0. Consider ...
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13 views

Bayesian Information Criteria variable penalisation for increasing N

I am trying to understand the Bayesian Information Criteria for model performance, given by the formula below: BIC=−2ln(L)+kln(n) I understand the aim is to minimize this function. I can see that ...
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137 views

Why is the penalty in the logistic regression likelihood ratio test different from the penalty I specified when fitting the model?

I'm fitting a penalized logistic regression model using the rms package in R. When I print the result, the penalty in the model likelihood ratio test is different from the penalty I used to fit the ...
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173 views

Penalized Negative Binomial- Subset selection and Coefficient estimation

I have a dataset with count variable of 50 observation and 260 independent variables. As the variance exceeds mean, I want to use Negative Binomial distribution. My objective is to build a model that ...
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3answers
744 views

Why does L2 regularization smooth the loss surface?

Fitting neural nets with L2 penalization, I've noticed that I often attain lower in-sample mean-squared errors with higher rates of L2 "weight decay", then I do with lower rates of L2 weight decay. ...
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17 views

Efficient Penalized MLE to Maintain Stationarity

I am trying to penalize a likelihood function, $-\log f(Y|\theta)$, to maintain stationarity of the autoregressive process. An vector autoregressive process is said to be stationary if the spectral ...
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1answer
50 views

$\ell_0$ penalised and $K$ sparse problems

Consider the $\ell_0$ penalized problem: $$\min_{x\in \mathbb{R}^n} \frac{1}{2}\|Ax-b\|_2^2+\lambda\|x\|_0 \qquad \qquad \qquad \qquad \qquad \qquad (1)$$ and $K$-sparse problem $$\min\frac{1}{2}\|Ax-...
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1answer
176 views

Maximizing (and derivating) log-likelihood of penalized logistic regression

I'm trying to solve Exercise 18.3 of "Elements of Statistical learning" by Hastie et al. and I'd be really grateful for any hints. Show that the fitted coefficients for the regularized multiclass ...
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2answers
2k views

B-Splines VS high order polynomials in regression

I do not have a specific example or task in mind. I'm just new on using b-splines and I wanted to get a better understanding of this function in the regression context. Let's assume that we want to ...
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1answer
172 views

Confidence intervals with penalized likelihood

I am trying to perform parameter estimation using something like a maximum likelihood ratio method, however I need to add a penalty term to constrain nuisance parameters which describe certain ...
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0answers
195 views

Does the SCAD penalty solve the issue of multicollinearity?

Is the SCAD penalty by Fan and Li (2001) able to solve the issue of multicollinearity and why? I read a paper published on the Journal of Financial Econometrics, “Asset pricing with a general ...
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1answer
61 views

Group lasso penalization

In group lasso we try to minimize the following $$\frac{1}{2}\|Y - \sum_{i=1}^JX_j\beta_j\|^2 + \lambda\sum_{i=1}^J\|\beta_j\| $$ Often they change this to $$\frac{1}{2}\|Y - \sum_{i=1}^JX_j\beta_j\|^...
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1answer
70 views

imputation with penalized (Cox) regression

I'm doing penalized (elastic net) Cox regression. But I also have missing data. Now, as I understand it, the reason we do multiple imputation is that once we do single imputation, our data points are ...
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2answers
1k views

Rare Events Logistic Regression

Suppose the event of interest occurs in approximately $10 \%$ of the cases where the number of cases is around $5,000$. Should you use a penalized logistic regression for this or is regular logistic ...
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1answer
40 views

LASSO for two types of variables: optimal tuning?

I have a location and scale linear regression model: $$y_j = x_j^T\beta + e_j,$$ where $e_j\sim N(0,\sigma_j)$, and $\sigma_j = \exp(x_j^T\theta)$, $j=1,...,n$, $x_j \in{\mathbb R}_p$, $\beta \in{\...
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0answers
283 views

Standardization in penalized regression using glmnet

I want to run a penalized multinomial logit and logit regression using the glmnet package in R. I understand, that before fitting the penalized model, one should ...
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2answers
142 views

LASSO for unit norm parameters?

I have the model $y = X\theta +e$, where $\vert\vert \theta\vert\vert =1$ and $e$ are iid normal errors and $\vert\vert\cdot\vert\vert$ represents the Euclidean norm. Can I use a LASSO penalty in this ...
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0answers
61 views

Only minimizers of quadratic penalized least squares can be linear

Question Define the matrix $A \in \mathbb{R}^{m \times n}$, the vector $b \in \mathbb{R}^m$, and the function $\mathrm{pen}: \mathbb{R}^n \to \mathbb{R}$. Then, put the minimizer $$\hat{x} = \arg\...