I have a training set of over a 100,000 points that is used to train a Logistic Regression Classifier (logit, since response is binary). The model is testing/fitted on a test set of 20,000 items. The test set is totally independent.   The ROC AUC value for this model is 0.85 which suggests that this is a good model. But I was not convinced. I picked a threshold $0.5$ (i.e., its classified positive if the model response $&gt; 0.5$, negative if model response $&lt; 0.5$).   At this threshold, I get the confusion matrix:  Confusion Matrix and Statistics            Reference Prediction     0     1          0 33307   679          1     0     0                 Accuracy : 0.98                              95% CI : (0.9785, 0.9815)     No Information Rate : 0.98                 P-Value [Acc &gt; NIR] : 0.5102                              Kappa : 0                 Mcnemar's Test P-Value : &lt;2e-16                        Sensitivity : 0.00000                      Specificity : 1.00000    So my question is, how good is the model if it is unable to predict a 'positive' class at 0.5 threshold?  My guess would be that the threshold of the model for labelling 'positive' is not $0.5$ in this case. Is this intuitive and make sense? Clearly the ROC AUC value is very high, which means that it does have a good TPR rate at lower thresholds.
This is a general question that was asked indirectly multiple times in here, but it lacks a single authoritative answer. It would be great to have a detailed answer to this for the reference.  , the proportion of correct classifications among all classifications, is very simple and very "intuitive" measure, yet it may be a . Why does our intuition misguide us here and are there any other problems with this measure?
Searching for questions that have ONLY a given tag (i.e. add a range operator for tags) Subtracting from a specific column Accepted way to abbreviate cities that have "Saint" in their name My first question here, so I'm not sure if this OT or not, so please bare with me.  Background: I don't live in US. I'm working with some data that I'm pulling from . Sometimes, I'm getting a city name as St. John and sometimes as Saint Ann.   So my question is, is there an accepted way on how people write a US city names which starts with Saint or is this just some random thing (or just specific to AdWords maybe)?  I'm asking this, because if for example I'll get both St. John and Saint John in the same file, should I consider them the same or should I be suspicious? Cannot access any files on Samsung Tab 4 7" Present tense in Flashback story for something that is still true now? I'm wondering whether I should use the present tense for a descriptive statement but in a past context. For example:     (1) I went to the zoo and saw a giraffe last week.       (2) A giraffe is a mammal with long neck.       (3) It is the first time I see that animal with my own eyes.   Statement (2) is a description of a giraffe in general, not the specific one in the zoo, so is it correct to use is?  Statement (3) is an event that is still true now, so should I use is and see?  I'm not native speaker so forgive me if the question is very obvious to others. Bootcamp: The startup disk does not have enough space to be partitioned When clicking continue on the first Boot Camp screen,  I am presented with a dialog that displays:     The startup disk does not have enough space to be partitioned.   You must have at least 39 GB of free space available.     This is despite "About this Mac" reporting 271GB of free space:    And "Disk Utility" reporting 268GB of free space:    Searching online I found  which suggested it was the result of Time Machine which i recently enabled and suggests to run sudo tmutil thinlocalsnapshots / 999999999999 which I did, it ran sucessfully, and I restarted, yet to no avail.  What is the solution to this instance of Apple's poor engineering?  Running macOS High Sierra 10.13.4 (17E202) How do I make my textures show in cycles? I am admittedly new to Blender, and of course cycles. I am working on a scene and I have textures set to my objects that render with internal engine just fine. However, when I go into cycles, everything is greyish. I have two light sources that should be sufficient (I think), I just don't know what I'm doing wrong. This is a screenshot of the cycles result. I'm married have a job with stable income.I have 2 kids. I have applied for UK visit visa about 7 years ago and was refused. I can't remember what exactly was the reason for refusal.  I want to travel for tourism to spend 9 days and my budget is around 1300GBP for the trip. I would be spending part of my annual leave in the UK. I have the following people in UK: Mother, Dad, Sister(she's married), Brother (married), Uncle and Aunt.  I'm travelling alone since my wife is pregnant. I haven't travelled since I was in school then.  I will be on my yearly 21 days annual leave during which I will be spending 9days in UK. I can't think of anything more about my circumstance.  So what should a cover letter look like?  secondly I have just 1 account where my salary is paid in monthly and my savings.I will be submitting the 6 months bank statement for the account.  Additional question:  In the income &amp; expenditure where one is asked to indicate if I have income and savings,should I click Yes or No. And if Yes should state the ending balance as at the time of my application. How can I serialize an object to JSON in JavaScript? How do I read / convert an InputStream into a String in Java? If you have a java.io.InputStream object, how should you process that object and produce a String?    Suppose I have an InputStream that contains text data, and I want to convert it to a String, so for example I can write that to a log file.  What is the easiest way to take the InputStream and convert it to a String?  public String convertStreamToString(InputStream is) {     // ??? } Bring Debian to second Position in the GRUB Menu at startup While I was reading Enderton's "A mathematical introduction to Logic", I came across the proof of the following sentence: "The set of all finite sequences of members of the countable set A is also countable".   Proof: The set S of all such finite sequences can be characterized by the equation  $$S=\bigcup_{n \in N} A^{n+1}$$ Since A is countable, we have a function f mapping A one-to-one into N. The basic idea is to map S one-to-one into N by assigning to $(a_0,a_1,...,a_m)$ the number $2^{f(a_0)+1}3^{f(a_1)+1}\cdot ... \cdot p_m^{f(a_m)+1}$, where $p_m$ is the $(m+1)$st prime. This suffers from the defect that this assignment might not be well-defined. For conceivably there could be $(a_0,a_1,...,a_m)=(b_0,b_1,...,b_n)$, with $a_i$ and $b_j$ in A but with $m\neq n$. But this is not serious; just assign to each member of S the smallest number obtainable in the above fashion. This gives us a well-defined map; it is easy to see that it is one-to-one.  Note: P is a finite sequence of members of A iff for some positive integer $n$, we have $P=(x_1,...,x_n)$, where each $x_i \in A$.  First of all, I cannot understand why the former assignment might not be well-defined and the latter assignment is well-defined. Secondly, I cannot understand what Enderton means by "just assign to each member of S the smallest number obtainable in the above fashion". By the way, is $(a,b,c,d) = ((a,b),(c,d))$ true? Also, in which cases can I omit/add parentheses in a tuple so as to have an equal tuple? I am very new to R. I am learning machine learning right now. Very sorry, if this question appears to be very basic.  I am trying to find a good feature selection package in R.  I went through Boruta package. It is a good package but I read that it is only useful for classification.  I want to do implement feature selection in R for regression tasks. I went through the caret package documentation but for my level, it is very difficult to understand.  Can any one please point me to a good tutorial or list any good packages or most frequently used packages in R for feature selection.  Any help would be appreciated. Thanks in advance. Rigid body simulation not interacting with objects that have an array modifier VS Code Salesforce plugin deploy does not provide an error message VS Code plugin for salesforce seems to be broken yesterday, It does not provide proper error message in case of failure.  Tried this in a developer org as well as scratch org. Neither deploy code or push gives an error message, and every time we need to go to Salesforce setup -> Deployment Status to view the details.  Is anyone aware of any workaround? Zero to the zero power – is $0^0=1$? $x^3-9=y^2$ find integral solutions Find all integral solutions  $x^3-9=y^2$  I tried many times but still no idea how to solve it. I will be grateful for any help. I use Lyx 2.1, document class : Report. My problem is that the titles of figures are written on the numbers at List of Figures. I'm looking to cite a number of web pages using bibtex and I was wondering if there was a specific template of the form @&lt;template name here&gt; for doing that. If you could use the following website as an example that would be great Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula As far as every question I've seen concerning "what is $\sum_{k=1}^nk^p$" is always answered with "Faulhaber's formula" and that is just about the only answer.  In an attempt to make more interesting answers, I ask that this question concern the problem of "Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula for fixed $p\in\mathbb N$".  I've even checked this  without finding what I want.  Rule #1: Any method to compute the sum in question for arbitrary $p$ is good, either recursively or in some manner that is not in itself a closed form solution.  Even algorithms will suffice.  Rule #2: I don't want answers confined to "only some values of $p$".  (A good challenge I have on the side is a generalized geometric proof, as that I have not yet seen)  Exception: If your answer does not generalize to arbitrary $p$, but it still generalizes to an infinite amount of special $p$'s, that is acceptable.  Preferably, the method is to be easily applied, unique, and interesting.  To start us off, I have given my answer below and I hope you all enjoy.