How valid is an approach of using LASSO to determine appropriate values to then use in a logistic regression that does not use any penalties?
I use Lasso logistic regression in order to identify a smaller subset of important variables. I start with N=51 (28/23) and 32 predictors.   So far it looks pretty promising, because I can identify four important predictors in my optimal model.   Now I would like to take those four predictors and examine them along with some control variables in a standard logistic regression.   My question is, does that analysis strategy make sense? Is there a better way to include controls or other variables that might be interesting?  For a better understanding:   Identify important variables via Lasso logistic regression Do further analysis including identified predictors and other control variables using standard logistic regression (using AIC to check model fit)
HTTP request parameters are not available by request.getAttribute() Are there any keyboard shortcuts for Windows 10 developer preview's virtual desktops ("Task View")? Prove $p_n(x) \rightarrow \sqrt{x}$ uniformly as $n \rightarrow \infty$ Define $(p_n)_n$ recursively by $p_0(x) = 0$ and $p_{n+1}(x) = p_n(x) + \frac{1}{2}(x - p_n(x)^2)$.  Prove that $p_n(x) \rightarrow \sqrt{x}$ uniformly for $0 \leq x \leq 1$ as $n \rightarrow \infty$.  I'm not sure where to go with this.  I can show inductively that $\forall n,\  0 \leq p_n(x) \leq 1$ for $0 \leq x \leq 1$, and I think that $p_n(x)$ is increasing with $n$, but I have no idea whether this helps me.  I know that I need to show that $\forall \epsilon&gt;0: \exists N \in \mathbb{N}: \forall n \geq N: \forall x\in [0,1]: \big|p_n(x) - \sqrt{x}\big| &lt; \epsilon$ Edit:  I just had a thought.  I'm given a version of Dini's theorem that reads  Let $X$ be a compact metric space, $(f_n)_n$ a sequence of real-valued continuous functions on $X$, $f$ a continuous function on $X$ such that: (i) $f_n \rightarrow f$ pointwise on $X$, and (ii) $f_n(x) \geq f_{n+1}(x) $ for all $x \in X, n \in \mathbb{N}$. Then: $f_n \rightarrow f$ uniformly on $X$.  Obviously, (ii) is not true for my sequence, but what if I took $f_n(x) = -p_n(x)$ and $f(x) = - \sqrt{x}$?  Then I could prove (ii) to be true, I know that $[0,1]$ is compact, and $f_n(x)$ is real-valued.  The only part I would need to prove is (i), which is where I get confused.  Correct me if I'm wrong, but after that I could say that since $(-p_n)_n \rightarrow -\sqrt{x}$, then $(p_n)_n \rightarrow \sqrt{x}$.  Any advice? Blender image output is greyish and not white I already searched the internet but could not find a solution to this. Maybe it is the same question as  but there was no answer.  I want to render a video with tracking, but the output "loses" color information and gets kind of greyish. I first thought that it is related to the renderer, but it happens in Cycles and Eevee. Therefore i made a sample image, added it to the image sequence editor and rendered it as 1 frame. Resulting in the same problem.  I placed the original image beside blenders output so that you can see the difference. The only idea I came up with is that something with the lighting is not correct but I can't find a setting for that.  I am using Blender 2.80 with the default settings. Only set the output resolution to match the input resolution. Blank screen after installing nvidia restricted driver I've  and rebooted my machine and now I get a black or blank screen.   How can I fix this? $\forall x,y>0, x^x+y^y \geq x^y + y^x$ Prove that $\forall x,y&gt;0, x^x+y^y \geq x^y + y^x$   A friend of mine told me none of the teachers in my school have succeeded in proving this seemingly simple inequality (it was asked at an oral exam last year). I tried it myself, but I made no significant progress. Saving Photoshop multilayer file to PDF without layers size difference Why is it that when I save a file that has many, many layers to a PDF without layers as a copy that the file size is larger than flattening the layers and then saving the file as a copy to PDF? 19Mb vs. 5Mb?? Wouldn't saving a file without layers be the same as flattening the layers and then saving the file?? Can anyone explain this? How to implement an abstract class in ruby? I know there is no concept of abstract class in ruby. But if at all it needs to be implemented, how to go about it? I tried something like...  class A   def self.new     raise 'Doh! You are trying to write Java in Ruby!'   end end  class B &lt; A   ...   ... end   But when I try to instantiate B, it is internally going to call A.new which is going to raise the exception.  Also, modules cannot be instantiated but they cannot be inherited too. making the new method private will also not work. Any pointers? How do I programmatically set the docstring? A strict equality operator will tell you if two object types are equal. However, is there a way to tell if two objects are equal, much like the hash code value in Java?  Stack Overflow question  is similar to this question, but requires a more academic answer. The scenario above demonstrates why it would be necessary to have one, and I'm wondering if there is any equivalent solution. Change the font of figure captions I would like to italicize my figure captions and make them smaller.  How can I do that? I am trying to construct a theoretical Diffie-Hellman key exchange protocol. However, i cannot understand the difference between choosing an additive group or a multiplicative group. I believe an additive would make it much more simple, but would a multiplicative group make it more difficult to break? What would be the difference between the use of those 2 kinds of number groups? CPU clock speed versus CPU core count - higher GHz, or more cores for SQL Server? We are beginning to provision a set of physical servers for a virtual cluster of SQL Server 2016 nodes within VMware. We will be utilizing Enterprise Edition licenses.  We plan on setting up 6 nodes, but there is a bit of a debate on what the ideal way to provision the physical servers with regards to CPU clock speed versus CPU core count.  I know this is largely dependent on transaction volume and number of databases stored among other software-specific factors, but is there a general rule of thumb that is advised?  For instance, is a dual 8-core, 3.2 GHz physical server (16 cores) more preferential to a dual 16-core, 2.6 GHz server (32 cores)?  Has anyone come across a white paper that further delves into this type of topic? Can the jQuery UI Datepicker be made to disable Saturdays and Sundays (and holidays)? I use a datepicker for choosing an appointment day.  I already set the date range to be only for the next month.  That works fine.  I want to exclude Saturdays and Sundays from the available choices.  Can this be done?  If so, how? How can I remove a suggestion from the Chrome address bar? I've got a couple of URL autocomplete suggestions where Chrome suggests the wrong URL consistently.   How can I delete the incorrect entry from the address bar's suggestion list? The page I want shows up too but it's never the first result. I'm looking for a way to prove $$\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^{2m+1}}=\frac{(-1)^m E_{2m}\pi^{2m+1}}{4^{m+1}(2m)!}$$ I know that $$\sum_{n=0}^\infty\frac{(-1)^n}{(2n+1)^{2m+1}}=\frac{1}{4^{2m+1}}\left(\zeta\left(2m+1,\frac14\right)-\zeta\left(2m+1,\frac34\right)\right)$$ so maybe I could simplify the above more? How to add home directory path to be discovered by Unix which command? string str1 = "12345ABC...\\...ABC100000";   // Hypothetically huge string of 100000 + Unicode Chars  str1 = str1.Replace("1", string.Empty);  str1 = str1.Replace("22", string.Empty);  str1 = str1.Replace("656", string.Empty);  str1 = str1.Replace("77ABC", string.Empty);   // ...  this replace anti-pattern might happen with upto 50 consecutive lines of code.   str1 = str1.Replace("ABCDEFGHIJD", string.Empty);   I have inherited some code that does the same as the snippet above. It takes a huge string and replaces (removes) constant smaller strings from the large string.  I believe this is a very memory intensive process given that new large immutable strings are being allocated in memory for each replace, awaiting death via the GC.  1. What is the fastest way of replacing these values, ignoring memory concerns?  2. What is the most memory efficient way of achieving the same result?  I am hoping that these are the same answer!  Practical solutions that fit somewhere in between these goals are also appreciated.  Assumptions:    All replacements are constant and known in advance Underlying characters do contain some unicode [non-ascii] chars Locking a file in Python Prove: $\displaystyle\sum_{k=1}^n k k!=(n+1)!-1$ (preferably combinatorially)   It's pretty easy to think of a story for the RHS: arrange $n+1$ people in a row and remove the the option of everyone arranged to height from shortest to highest, but it doesn't hold up for the LHS.   Alternatively, trying to visualize the LHS, I noticed that it's like a right angle tetrahedra:  1  2!+2!  3!+3!+3!  ...  But it doesn't help to see a connection to the RHS.  Note: no integrals or gamma function nor use of other identities without proving them nor generating functions.