15,572 reputation
13280
bio website linkedin.com/in/crntaylor
location London, United Kingdom
age 30
visits member for 3 years, 8 months
seen yesterday

I'm broadly interested in very applied math. I try to apply ideas from mathematics, statistics, machine learning, formal systems and computer science to solve real-world problems. Mostly in applied finance/quantitative trading, but in other areas if the mood takes me.


The following is for my own use, but feel free to borrow it -

Hi. It looks like you are new here. We are generally very willing to help, but we like users to show the work that they've done towards solving the problem on their own first. If you can edit your question to show the code you've written so far, and where you are stuck, then you will get a much better response.


Aug
7
comment Coordinate descent with constraints
Thanks Michael!
Aug
6
comment Coordinate descent with constraints
Thanks for this answer Michael. Is it easy to see that when dealing with coordinate-wise bounds, thresholding to $l_i\leq x_i\leq u_i$ at each step results in the global minimizer for the problem I posed (convex function with separable non-smooth constraints and coordinate-wise bounds)?
Aug
1
comment What are some conceptualizations that work in mathematics but are not strictly true?
@BCLC a physicist would say $f(r,\theta)=r^2$ whereas a mathematician would say $f(r,\theta)=r^2+\theta^2$.
Jul
28
comment Interview puzzle with a deck of cards, some cards upside-down
@Wonder Yes, it is the same answer (+1) - I saw that another answer appeared just as I was finishing mine, but since I'd already written it I hit 'post' anyway.
Jul
18
comment What numerical methods are known to solve $L_1$ regularized quadratic programming problems?
I'll certainly give it a shot. I've already tried several general-purpose solvers (open source and commercial) which have been okay, but not as fast as a couple of hand-rolled special-purpose solvers. I've not tried CVX yet though...
Jul
18
comment What numerical methods are known to solve $L_1$ regularized quadratic programming problems?
Thanks Michael, this is really helpful - I'm exploring several different options you suggested. I never have to solve a particularly tricky problem (mostly quadratic programming with an $L_1$ term and sometimes linear inequality constraints) but I need to solve a lot of them, so speed is a factor for me. Thanks for your help!
May
21
comment A fair coin is flipped 2k times. What is the probability that it comes up tails more often than it comes up heads?
It seems likely that the "2k" in the question refers to a general even number $2k$ rather than "2000".
May
7
comment Help with 2 questions my professor gave us
For (i) assume there are two solutions $a,b$ s.t. $a^2=r$ and $b^2=r$ with $a\neq b$. Then either $a>b$ or $a<b$. Can you derive a contradiction?
May
6
comment How to draw contour lines for a bivariate Gaussian distribution by hand!
Are you talking about a 2d gaussian distribution?
Mar
5
comment Game Theory/Bayesian approach to a bluffing game
@DanielR Pretty sure (although open to being proved wrong). Player 1's expectation, if he bluffs with probability $q$, is $E = 0.2(2p + (1-p)) + 0.8(q(-p + (1-p)))$ which simplified to $E=0.2(1+p) + 0.8q(1-2p)$. Therefore if $p>0.5$ the second term is negative, so $q=0$ maximizes the expectation. If $p<0.5$ the second term is positive, so $q=1$ maximizes the expectation. This assumes that player 2 never changes their strategy, of course.
Mar
4
comment What is equivalence of $(p \vee q) \wedge \neg (p \vee q)$?
Let $a = p \vee q$. Then you have $a \wedge ¬ a$.
Feb
21
comment How do you describe your mathematical research in layman's terms?
@Arthur Feynman was speaking about theoretical physics, which deals with quarks, gluons, hadrons, bosons and other things that most people aren't familiar with. His book QED succesfully imparted the flavour of quantum electrodynamics and the path integral formalism to me as a sixteen year old. I don't think we should shrug off our responsibility as mathematicians so easily.
Feb
18
comment Standard Deviation Annualized
@kookster Yes, still true (note that with only 30 data points the confidence intervals on your measured standard dev will be quite wide).
Feb
1
comment integration method
This transformation gives better convergence properties for the algorithm described in your code (which is essentially Gaussian quadrature at random locations) but that's not what I understand by the "hit and miss" method (generating random $(x,y)$ pairs and checking to see if they fall into the region being integrated).
Feb
1
comment integration method
This answer from over two and a half years ago suddenly got a flurry of upvotes - anyone know why?
Jan
31
comment Is this number rational or irrational?
@HagenvonEitzen Thanks. This question was actually inspired by this topic on Hacker News.
Jan
31
comment Coin flipping probability game ; 7 flips vs 8 flips
I would also be perfectly willing to accept the intuitive explanation as a proof. In fact, it's a strictly better proof than the one given, because it immediately generalizes to the case where your friend flips $n$ times and you flip $n+1$ times for $n\geq 0$.
Jan
31
comment Is this number rational or irrational?
@Martín-BlasPérezPinilla How long did it take you to come up with this argument? Did you see it instantly?
Jan
28
comment Few calculus questions
Hi. It looks like you are new here. We are generally very willing to help, but we like users to show the work that they've done towards solving the problem on their own first. If you can edit your question to show what you've done so far, and where you are stuck, then you will get a much better response.
Jan
15
comment Why isn't $\int\sin(ix)~dx$ equal to $i\cos(ix)+C$ ?
@Lucian The law in the land of Mathematics is "unequal until proven equal" ;)