When using regularization wouldnt it make all parameters very small? In regularization, we add square of thetas multiplied by lambda(excluding theta_0). The value of lambda is high because values of theta should be close to zero to neglect the value of its associated feature. Now my question is when we apply gradient descent to set the values of theta which will result in best fit to data. Wouldn't it also reduce the values of all the thetas (which we don't want to reduce)? Because we are adding every value of theta at the end of the cost function. Which will result in a very low slope linear line causing underfitting.
Why does shrinkage work? In order to solve problems of model selection, a number of methods (LASSO, ridge regression, etc.) will shrink the coefficients of predictor variables towards zero. I am looking for an intuitive explanation of why this improves predictive ability. If the true effect of the variable was actually very large, why doesn't shrinking the parameter result in a worse prediction?
Why are the rooting apps not working anymore? A couple years ago, it was easy to root any device: Install KingRoot, KingoRoot, or a similar app, hit the large ROOT button, and let it do the rest. After 5 minutes or so, a green "Root Succeeded!" prompt will pop up, and we can choose to keep the root app, or uninstall it and install a clean root manager app like SuperSU/Superuser.  How do they work? Why aren't they working anymore? And if they work, should I use them or not? Is it okay to use my US visa after a name change? How to find application's path from command line? For example, I have git installed on my system. But I don't remember where I installed it, so which command is fit to find this out? Given the functional dependencies of a relation is there more then one way to normalize it? Add a binary to my path I have an executable. I want to execute the executable in terminal with name only like other commands.  I can put my executable in /usr/local/bin or I could add its PATH to ~/.bashrc. Both will work.  What is better?  Is there  any difference? Syntax of Using Math Mode: Empty Lines (Beginner Question) I'm just starting to learn LaTeX. I tried typing \begin{equation*}  (math goes here)  \end{equation*}  and I got a whole bunch of errors. It seems LaTeX interpreted the empty line as the equation: when it saw nothing there, I guess it just ended math mode? It then said my other commands needed $'s so I assume that's what happened. When I typed \begin{equation*} (math goes here) \end{equation*}  everything was fine. So I'm confused. If LaTeX sees an empty line in an environment, does it just interpret this as me changing my mind, and deciding not to use the declared environment? "Outside" or "outside of"? I want to create a animation like those "spacetime deformation" ones, but I am stuck on creating "spacetime".  (a mesh/plane).  I created a plane, gave it a soft body, collisions, and a passive rigidbody.    A cube with a rigidbody and collisions will land and deform the mesh, but it snaps right back.  How can I make it so the cube lands, and then leaves the plane deformed, and the cube just sits there?  I googled around and searched this site, nothing comes up.  An image of what I want (after it settles):    The ball depressed the mesh, creating an indentation. Can I check iPhone, iPad, Watch battery on Mac? My goal is to have battery status of other Apple device on my Mac (preferably on menubar). I'd like to have a glimpse of the battery status of my iPhone, iPad, Watch, and Airpods.  I'm a user of Bitbar and iStat menu, but I haven't found any widgets can wirelessly check other Apple device's battery status.  What I know is that I can click the Wi-Fi icon on menu bar and it will show my iPhone battery status. To show the percentage, I have to option + click the Wi-Fi icon and hover over my mouse on the iPhone hot spot section. It's pretty clunky, but I guess at least the API is there.  I am also open to third party apps which can let me see battery status across devices. Time reversal symmetry and T^2 = -1 Proving trigonometric equation $\cos(36^\circ) - \cos(72^\circ) = 1/2$ Please help me to prove this trigonometric equation.  $\cos \left( 36^\circ \right)-\cos \left( 72^\circ \right) = \frac{1}{2}$  Thank you. Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a < 23$. Solve $[2^{(2^{403})}] = [a]$ in $\mathbb Z_{23}$ where $0 \le a &lt; 23$.  I've tried to combine corollaries of Fermat's little theorem and various other methods to solve this, but have always been stuck. A. These kinds of problem are to be avoided. B. These kind of problems are to be avoided.  Are both A and B grammatical? If not, why not? If so, after having noticed the parallelism between A and C, and between B and D, could we say that C and D are &quot;standard&quot; English, too?  C. These kinds of problem are ones to avoid. D. These kind of problems are ones to avoid. Meaning of the word "axiom" Thus, axioms are propositions we assume to be true and we use them in an axiomatic theory as premises to infer conclusions, which are called "theorems" of this theory.  For example, we can use the  to prove theorems of arithmetic.  This is one meaning of the word "axiom". But I recognized that the word "axiom" is also used in quite different contexts.  For example, a group is defined to be an algebraic structure consisting of a set $G$, an operation $G\times G\to G: (a, b)\mapsto ab$, an element $1\in G$ and a mapping $G\to G: a\mapsto a^{-1}$ such that the following conditions, the so-called group axioms, are satisfied:   $\forall a, b, c\in G.\ (ab)c=a(bc)$, $\forall a\in G.\ 1a=a=a1$ and $\forall a\in G.\ aa^{-1}=1=a^{-1}a$.      Why are these conditions (that an algebraic structure has to satisfy to be called a group) called axioms? What have these conditions to do with the word "axiom" in the sense specified above? I am really asking about this modern use of the word "axiom" in mathematical jargon. It would be very interesting to see how the modern use of the word "axiom" historically developed from the original meaning.   Now, let me give more details why it appears to me that the word is being used in two different meanings:  As peter.petrov did, one can argue that group theory is about the conclusions one can draw from the group axioms just as arithmetic is about the conclusions one can draw from the Peano axioms. But in my opinion there is a big difference: while arithmetic is really about natural numbers, the successor operation, addition, multiplication and the "less than" relation, group theory is not just about group elements, the group operation, the identity element and the inverse function. Group theory is rather about models of the group axioms. Thus: The axioms of group theory are not the group axioms, the axioms of group theory are the axioms of set theory.  Theorems of arithmetic can be formalized as sentences over the signature (a. k. a. language) $\{0, s, +, \cdot\}$, while theorems of group theory cannot always be formalized as sentences over the signature $\{\cdot, 1, ^{-1}\}$. Let me give an example: A typical theorem of arithmetic is the case $n=4$ of Fermat's last theorem. It can be formalized as follows over the signature $\{0, s, +, \cdot\}$: $$\neg\exists x\exists y\exists z(x\not = 0\land y\not = 0\land z\not = 0\quad\land\quad x\cdot x\cdot x\cdot x + y\cdot y\cdot y\cdot y = z\cdot z\cdot z\cdot z).$$ A typical theorem of group theory is  which states that for any finite group G, the order of every subgroup H of G divides the order of G. I think that one cannot formalize this theorem as a sentence over the "group theoretic" signature $\{\cdot, 1, ^{-1}\}$; or can one? Replace values which obey certain criteria Performance differences between equal (=) and IN with one literal value How to import Apple Mail archive files in Outlook 2013? I need to import Apple Mail archived files in Outlook 2013 on Windows, but every time I open the import wizard and reach the file selection step, I cannot select the archived file. It doesn't even show in the dialog box.  I don't know what the issue is. Is it the file size issue as the archive file is large (about 7 GB) or there is any other fault? How to use Terminal to delete all .svn folders recursively? What command can I type into the Terminal so that I can delete all .svn folders within a folder (and from all subdirectories) but not delete anything else? I tried this in mysql:  mysql&gt; alter table region drop column country_id;   And got this:  ERROR 1025 (HY000): Error on rename of './product/#sql-14ae_81' to './product/region' (errno: 150)   Any ideas? Foreign key stuff? Is the sentence "There is a large number of labourers who want to migrate to Japan for work." correct? Possible Duplicate:             There is a large number of labourers who want to migrate to Japan for work.   I type this sentence in a word processor, and it reports an error that "is" should be "are" (subject-verb agreement).  I doubt this is a valid error. Could anyone confirm this?