In the world of sphere packing, thereβs been debate about whether order or a dash of chaos will give the best results. A recent proof marks a win for order. www.quantamagazine.org/new-sphere-p...
And a recent very well written review of NS:
"Nested sampling for physical scientists"
arxiv.org/abs/2205.15570
Nested Sampling is extremely popular in some communities, and there are often claims that it helps mitigate "phase transition" issues that can often affect standard geometric "tempering" methods (although I do not understand that well enough yet...) It's great to see explicit connections with SMC!
"Unbiased and Consistent Nested Sampling via Sequential Monte Carlo"
by Robert Salomone, Leah F. South, Christopher Drovandi, Dirk P. Kroese, Adam M. Johansen
arxiv.org/abs/1805.03924
"A simpler nested sampling identity"
Interesting blogpost on nested sampling & SMC by Nicolas Chopin
statisfaction-blog.github.io/posts/04-06-...
See you in πΈπ¬
My bad, this wasn't clear. It's in the space of all probability densities
Motivated by the reading of this nice article:
"Sequential Monte Carlo approximations of Wasserstein--Fisher--Rao gradient flows"
by Francesca R. Crucinio, Sahani Pathiraja
arxiv.org/abs/2506.05905
And here is how the geodesic path looks like (again under the Fisher-Rao metric)
Here's how the gradient flow for minimizing KL(pi, target) looks under the Fisher-Rao metric. I thought some probability mass would be disappearing on the left and appearing on the right (i.e. teleportation), like a geodesic under the same metric, but I was very wrong... What's the right intuition?
Once you have tried symplectic integrators, you never go back.
The full (?) program of talks etc. for BayesComp seems to be online now (bayescomp2025.sg#programme), and looks pretty exciting - I will need to set aside some time to carve out my own schedule!
Once the prompt is public, I do not think it will provide much signal (but it could potentially slightly help some the papers make sure their writing style align well with the conference expectations)
How to implement this in practice, make the "review" prompt public in advance?
<proud advisor>
Hot off the arXiv! 𦬠"Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation" π Appa is our novel 1.5B-parameter probabilistic weather model that unifies reanalysis, filtering, and forecasting in a single framework. A thread π§΅
These sparse Gaussian Processes have been around longer than some grad students, but still fun to code! (and today was my first time coding one...)
Today, re-reading a classic.. the 1953 paper that started it all
Is it based on the last year's preprint by Huhtikuun Typerys?
extracted from:
"Upper Bounds for the Connective Constant of Self-Avoiding Walks" by Sven Erick Alm
www.cambridge.org/core/journal...
Cute way to upper bound the connective constant of Z^d. For some length L, enumerate {w_1, w_2, ... , w_N} the Self-Avoiding-Walks of size L. An upper bound is given by the largest eigenvalue of the NxN matrix where M_{i,j}=1 iff there is a SAW of size (L+1) that starts with w_i and ends with w_j.
Ah, but this paper seems to be confident that the conjecture is wrong, based on extensive simulations for estimating the connective constant up to 12 decimals (at which point there is a departure from the conjectured value). Still open though π
arxiv.org/pdf/1607.02984
Conjecture dates from 1992:
"Algebraic Techniques for Enumerating Self-Avoiding Walks on the Square Lattice"
arxiv.org/abs/hep-lat/...
"While we consider it would be fortuitous if this were the true value of the critical point, it nevertheless provides a useful mnemonic" π
Approximating N(L), the number of Self-Avoiding-Walks in Z^2 of length L, is an assignment in my Simulation course this year. The connective constant is:
C = \lim N(L)^1/L ~ 2.638..
Still open-problem to this day: is it true that 1/C equals the zero of the polynomial P(x)=581*x^4 + 7*x^2 - 13 π±
That's interesting that it seems like very little is known about the asymptotic of the second largest increasing subsequence (and no fast method to compute it)
This fast way of finding the LIS is neat! Just tried to reproduce your nice plot without leaving the phone π
chatgpt.com/share/67e8ec...
Sequential Monte Carlo (aka. Particle Socialism?):
"why send one explorer when you can send a whole army of clueless one"
Next week is the MCMC chapter of my simulation course. Asked chatgpt to come up with a funny drawing:
I already advertised for this document when I posted it on arXiv, and later when it was published.
This week, with the agreement of the publisher, I uploaded the published version on arXiv.
Less typos, more references and additional sections including PAC-Bayes Bernstein.
arxiv.org/abs/2110.11216
Are you at AAAI in Philadelphia and interested about #tensor-factorizations or #circuits or even both?
Then join us today at our tutorial: "From tensor factorizations to circuits (and back!)"
Details and materials here
april-tools.github.io/aaai25-tf-pc...
Time 4:15pm - 6:00pm, Room 117
New video! Terence Tao on how we measure the cosmos: youtu.be/YdOXS_9_P4U
