I am looking for some suggestions on what methods are appropriate for training a dataset with a high skew in the outcome classes. The ratio of Class 0: Class 1 is about 20:1 and I am looking to maximize the accuracy for identifying Class 1 outcomes. This is similar to oft discussed topics such as cancer detection.  I have used some methods before but am trying to find if there is any comprehensive resource / suggestions that talks to the different methods for these cases. Examples of how they are applied in R (packages, etc) or with caret would be useful. It is a sparse dataset with about 100K examples of which 5000 belong to Class 1 and the rest to Class 0. Each example has about 20 features, and includes null values.
We already had multiple questions about unbalanced data when using , , ,  and a number of other similar questions, what makes it a very popular topic! Unfortunately, each of the questions seems to be algorithm-specific and I didn't find any general guidelines for dealing with unbalanced data.  Quoting , dealing with unbalanced data     (...) heavily depends on the learning method. Most general purpose   approaches have one (or several) ways to deal with this.   But when exactly should we worry about unbalanced data? Which algorithms are mostly affected by it and which are able to deal with it? Which algorithms would need us to balance the data? I am aware that discussing each of the algorithms would be impossible on Q&amp;A site like this, I am rather looking for a general guidelines on when it could be a problem.
I am travelling to Athens, Greece, shortly, and have seen . Should I be worried? Should I cancel my trip?  Update  It's fine, taxis are currently on strike, but Syntagma Sqaure is fine: How to prove the midpoint of a chord is also the midpoint of the line segment defined by the points of intersection of other two chords with it? "Your python3 install is corrupted" I want to upgrade from Ubuntu 16.04.5 LTS to 18.04, so ran sudo do-release-upgrade. After downloading and extracting bionic.tar.gz I get:  Can not upgrade   Your python3 install is corrupted. Please fix the '/usr/bin/python3' symlink.   I saw  and so I did sudo ln -sf /usr/bin/python3.6 /usr/bin/python3 thinking that it would be a similar problem. But that didn't work (still same error message).  I have a few python versions:  $ ls /usr/lib | grep python python2.7 python3 python3.5 python3.6  $ update-alternatives --display python3 python3 - auto mode   link best version is /usr/bin/python3.6   link currently points to /usr/bin/python3.6   link python3 is /usr/bin/python3 /usr/bin/python3.5 - priority 1 /usr/bin/python3.6 - priority 2   How do I fix python3? How do I Uninstall Windows 10 or Windows 10 preview? Let $\alpha, \beta \in \mathbb{C}$, such that $\alpha + \beta$, and $\alpha\beta$ are algebraic. Show that $\alpha$ and $\beta$ are algebraic. Let $\alpha, \beta \in \mathbb{C}$,  such that $\alpha + \beta$, and $\alpha\beta$ are algebraic. Show that $\alpha$ and $\beta$ are algebraic.   attempt: Suppose $\alpha, \beta \in \mathbb{C}$ such that $\alpha + \beta$, and $\alpha\beta$ are algebraic.  Let $\alpha + \beta$, $\alpha\beta$ are algebraic be algebraic over $F$. And let $\alpha, \beta \in K$, where $K$ is an extension of $F$.  then $\alpha + \beta $ and $\alpha\beta$ lie in the extension $K = F(\alpha,\beta)$, which is finite over $F$.  so $[F(\alpha, \beta) : F] = [F(\alpha, \beta): F(\alpha + \beta, \alpha\beta)][F(\alpha + \beta, \alpha\beta) : F] \leq 2[F(\alpha + \beta, \alpha \beta) : F] $, since $\alpha + \beta$ and $\alpha \beta$ are roots .   So $[F(\alpha + \beta) : F]$ is finite and in the extension $F(\alpha,\beta)/F$ the elements must be algebraic over $F$, then $\alpha , \beta$ are algebraic.  Can someone please verify this? Or help me give a better approach. Thank you! Something wrong with monthly user rep - some users show quarterly figures? Is there an official rule that the minimum damage can't be negative? A slightly humorous thought occurred to me (a recovering rules lawyer) after reading .     "None of the answers actually specify that 0 is the minimum damage."   Logically it wouldn't make sense for an attack to apply negative damage or healing, except in specific cases like hitting a flame elemental with a fire attack. Ruling that you could do negative damage would lead to an exploit to avoid costs of healing. As such I highly doubt any DM would make such a ruling. I definitely wouldn't except for the most absurd and humorous of games were failure is the expected result not success.  Another possibility (as suggested by Secespitus) is that negative damage would reflect back on the attacker. This could be seen as punching a strongman so hard (or in just the wrong way) as to injure your own hand.  This would also play well in a failure is the only option game, and if there is a rule suggesting that it would be an appropriate answer to this question as well.  Take the case of a person with less than 8 Strength, no levels in monk, and does not have a tavern brawler.  Would they do -1(1 - 2) damage on unarmed strikes? If so what would the result of the negative damage be?   "Healing" the target because such a puny hit actually raises their fighting spirits and makes them more capable of fighting Reflective Damage, the attacker actually takes 1 point of damage, representing injury to his hand or other damage   I am curious to know if there is an official rule stating that the minimum damage an attack can do is 0 or is there something in the damage calculation that I am missing that would otherwise prevent negative damage? The  (click on your number of helpful flags in your profile) is cool, however some posts have a gray background, some don't. What does it mean?  example: Our company has multiple domains set up with one website hosted on each of the domains. At this time, each domain has its own authentication which is done via cookies.   When someone logged on to one domain needs to access anything from the other, the user needs to log in again using different credentials on the other website, located on the other domain.   I was thinking of moving towards single sign on (SSO), so that this hassle can be eliminated. I would appreciate any ideas on how this could be achieved, as I do not have any experience in this regard.  Thanks.  Edit: The websites are mix of internet (external) and intranet (internal-used within the company) sites. How do I access previous promise results in a .then() chain? Modify footer used by elsarticle.cls Word for "blissfully oblivious"? Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group. Prove that $(\mathbb{Z}_n , +)$, the integers  $\pmod{n}$ under addition, is a group.  To show that this is a group, I know I need to show three things (in our text, we do not need to show that addition is closed-- rather, we show these three items):  $(a)$ Associative Law  $(b)$ Existence of Identity  $(c)$ Existence of Inverse  This is what I have been working with so far:     $(a)$ Associative Law:   First, assume that $n$ is a composite number and that $a,b \in \mathbb{Z}$ s.t. $a=nx$ and $b=ny$ for some integers, $x$ and $y$. Then $a+nx+nx=n(x+y)$.     So, this is where I am stuck for the Associative Law. I'm not sure if I am headed down the correct path to show that $\mathbb{Z}_n$ is associative.      $(b)$ Existence of Identity:   Generally, when showing the existence of an identity we can use this information for addition :  $a + 0 = 0 + a =a$.    I am unsure how to insert the modular portion of the definition into the existence of this identity. I realize that for addition, we generally look at $0$ (rather than $1$ for multiplication).     $(c)$ Existence of Inverse: I need to show that for each element $a \in \mathbb{Z}_n$ that $a^{-1}=-a$. Again, I do not know how to insert the modular portion of definition into this aspect of the proof.   My question is how to incorporate this modular information into the proof that this is a group. We have not covered the integers modulo $n$, binary operations, nor groups in my intro to proofs course. I am trying to read my text to figure out how to prove this, but have a difficult time reading and interpreting math speak. Conjugate subgroup strictly contained in the initial subgroup? How to combine bold and "code sample" in Markdown? Index with exercise numbers How to provide a file download from a JSF backing bean? What is the difference between a relative phase and a global phase? In particular, what is a phase? I know that $re^{i\theta} = x + iy$ for any complex number $x + iy$ by Euler's formula. How do you calculate relative and global phase? I have been thinking about the following formulation of the Axiom of Choice.:     For any relation $R$, there is a function $H$, which is a subset of $R$, and such that $\operatorname{dmn}H=\operatorname{dmn}R$.   At first, it seemed surprising to me that this did not follow from Comprehension (i.e., from the schema  $\forall x_1, x_2, ..., x_n \forall C\exists B \forall x ( x \in B \Leftrightarrow x \in C \land \phi )$, where $B$ does not occur free in $\phi$).    I thought that for any relation, it seems that we should be able to define a subset of it with the same domain meeting a "functional condition".  But when I tried to do this, I couldn't.  However, I felt like I was getting close when I let $B$ be free in $\phi$, i.e., when I let myself say that $w$ is in $R$ and also anything in $H$ meets such and such conditions, where $H$ is the set (function) whose existence I'm trying to prove.    But my understanding is that Choice does not even follow from Naive Comprehension.  So, I wondered if someone could explain the following precisely.   Why does the above formulation of Choice does not follow from regular Comprehension? Why does it not even follow from Naive Comprehension (assuming that it does not)? What is the difference between the Bash operators [[ vs [ vs ( vs ((? I am a little bit confused on what do these operators do differently when used in bash (brackets, double brackets, parenthesis and double parenthesis).  [[ , [ , ( , ((   I have seen people use them on if statements like this :  if [[condition]]  if [condition]  if ((condition))  if (condition)