Premise  I saw an interesting example of a machine learning logistic classifier for modeling/predicting sentiment for customer reviews. One of the first things in the example was a note on probabilities. Namely, how many reviews were thought to be positive (user liked the product). It was denoted as the following math notation, which is followed by a quote:  $P(y=1)=.7$     Degrees of belief: "I expect 70% of rows to have y=1 (exact number   will vary for each specific dataset, as each dataset would be a   different subset of the underlying population)   When I think about that, it seems to makes sense at surface level, the math concerning probabilities/conditional probabilities aren't too overbearing, but my intuition hasn't been able to reconcile exactly why this information is important. Assuming two outcomes: y=0 and y=1, P(y=1)=.7 would mean 70% of reviews are positive and 30% are negative. If we have a large enough sample size, we could expect the population values to be in the neighborhood of this. Maybe it's .7 or .5; I don't see how it changes how we estimate our coefficients for the model. To me, it just seems like a fun-fact, like I said, I don't see how I'm supposed to use this information during implementation.  The only thing I could think of is that if P(y=1)=.0001 or some really small number, that would mean we have a noticeable case of class imbalance and that could affect classification accuracy (some models are more robust to class imbalance than others). While this is an important consideration, and would probably merit finding P(y=1), I still can't help but wonder is there anything else...  Question  How can we best utilize the knowledge of P(y=1) in classification?  Further Clarification:  Answers may expand on P(y=1) as it relates to any of the following:   heuristic for model accuracy weights for model model selection
I have a question regarding classification in general. Let $f$ be a classifier, which outputs a set of probabilities given some data D. Normally, one would say: well, if $P(c|D) &gt; 0.5$, we will assign a class 1, otherwise 0 (let this be a binary classification).   My question is, what if I find out, that if I classify the class as 1 also when the probabilities are larger than, for instance 0.2, and the classifier performs better. Is it legitimate to then use this new threshold when doing classification?  I would interpret the necessity for lower classification bound in the context of the data emitting a smaller signal; yet still significant for the classification problem.  I realize this is one way to do it. However, if this is not correct thinking of reducing the threshold, what would be some data transformations, which emphasize individual features in a similar manner, so that the threshold can remain at 0.5?
Changing "index.php" Within The Address I installed the latest Ubuntu today, 15.04. Spotify has stopped working. How can it be made to work again?  The Unity bar flashes green 4 or 5 times and then stops flashing. There are no error messages. It was installed successfully and played well on 14.10 till the upgrade a few hours ago. It just does not appear on the screen. Can someone explain a stock's "bid" vs. "ask" price relative to "current" price? In my online brokerage account, I want to buy a particular stock and I see the following:  Bid:  13.20 x200           Ask:  13.27 x1,000   the current stock price is 13.22.   Can someone explain what the bid and ask prices mean relative to the current price?  If I buy 1000 shares, why would I pay more? Best way to center a &lt;div&gt; element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too? How can I initialise a static Map? How would you initialise a static Map in Java?  Method one: static initialiser  Method two: instance initialiser (anonymous subclass) or some other method?  What are the pros and cons of each?  Here is an example illustrating the two methods:  import java.util.HashMap; import java.util.Map;  public class Test {     private static final Map&lt;Integer, String&gt; myMap = new HashMap&lt;&gt;();     static {         myMap.put(1, "one");         myMap.put(2, "two");     }      private static final Map&lt;Integer, String&gt; myMap2 = new HashMap&lt;&gt;(){         {             put(1, "one");             put(2, "two");         }     }; } How to view recently opened media files? In windows we have an option to view recently opened media files as my recent documents, I was  wondering does there exists something like that in Ubuntu?  via terminal or via GUI? Can I use lens brand X on interchangeable lens camera brand Y? What kind of capacitor could build up, and maintain a charge acquired from lightning? So basically this proof centers around proving that (S,*) is a group, as it's quite easy to see that it's abelian as both addition and multiplication are commutative. My issue is finding an identity element, other than 0. Because if 0 is the identity element, then this group won't have inverses.  The set explicitly excludes -1, which I found to be its identity element, which makes going about proving that this is a group mighty difficult. The rules on  state:     Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum [...]   Does this only apply if you aren't already at 0 HP? Or rather, what happens if you are currently at 0 HP and take massive damage? How do I set a background image while I am editing? How do I put a backdrop behind the model that I am creating so that I can compare the picture to the model while editing? When to use \par and when \\, \newline, or blank lines What is the difference between \par, \newline, \\ and blank lines? When should I use which one? Accessing a property of derived class from the base class in C# What is the view on accounts shared by multiple users on Stack Overflow? It has been my understanding that accounts are suppose to be for a specific user. This user, , is a company: . No doubt, this account has provided some quality answers. However, if a specific user cannot be identified, I don't think that the rep gain, rewards, or badges should be given. This should somehow be tagged as a 'Corporate User'. The rep has no real value when you can't be somewhat sure that the same person is giving the answers all the time.  This is where I found an answer by Devart: , peddling a product.    Edit 2 Good points have been brought up and most I can agree with. But we are setting a precedent. Meta Fudgey brought up a good point about the account's ability to use mod tools responsibly and consistently. Maybe this feature is not available to an account that appears to be an umbrella account unless a single user is identified. I think it is important to consider this aspect.    Let me re-iterate: the user(s) has provided excellent content and I would want that to continue. However, there is more at stake here than meaningful content and helpful resources.      Edit The view on 'shared' accounts wasn't so bright a year ago. For most of us, we have information in our profiles that identifies us as individuals. No, I don't have absolute knowledge of the activities on this account and how many people might use it. Meh, for all we know it could be a knowledgeable programmer with some good PR sense. On the other hand, it could be a PR person with no programming knowledge getting the answers from an employee. Who knows... What does this box icon represent? Since I started playing, I have seen this icon in the bottom right of my screen. Clicking it does nothing.  What does this icon represent?  I'll add a PC tag, as I'm playing on PC, and it could be related to that. irreducibility of a polynomial over $\mathbb{F}_2$ Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)? Selection of logical connectives {¬,∨,∧,⇒,⇔} in set theory? Proof of the uncountability of reals using the diagonal argument—problem?