Moritz Schauer @MoritzSchauer Twitter profile

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Moritz Schauer

@MoritzSchauer

8 months

Apparently this is my claim to fame

depths of wikipedia!

@depthsofwiki

2 years

obsessed with whoever saw gum on a sidewalk and was like "let me add this to the poisson distribution wikipedia article"

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Last Seen Profiles

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@aiiiep

Moritz Schauer

@MoritzSchauer

1 year

📣 Announcing a new working paper on 𝒟𝒾𝒻𝒻𝑒𝓇𝑒𝓃𝓉𝒾𝒶𝒷𝓁𝑒 Metropolis-Hastings 🧵

Differentiating Metropolis-Hastings to Optimize Intractable Densities

We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers, allowing us to differentiate through probabilistic inference, even if the model has discrete components...

arxiv.org

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Moritz Schauer

@MoritzSchauer

1 year

Causal discovery using Julia: A brief introduction, a simulation, and a possible use case (using Causalinference.jl)

Causal discovery using Julia: A brief introduction, a simulation, and a possible use case

In situations where the causal structure a dataset is unknown, algorithms can be used to estimate DAGs for use in causual inference.

towardsdev.com

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Moritz Schauer

@MoritzSchauer

1 year

Ahaha nice: Malliavin calculus, so far mystery to me, is combining the score method aka REINFORCE with the likelihood from Girsanov's theorem to estimate gradients of expectations!

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Moritz Schauer

@MoritzSchauer

2 years

How to do differentiable programming if programs are using discrete random variables (e.g. for optimising a random choice the program takes)? @ChrisRackauckas with a thread about our new paper

Dr. Chris Rackauckas

@ChrisRackauckas

2 years

Differentiable programming (dP) is great: train neural networks to match anything w/ gradients! ODEs? Neural ODEs. Physics? Yes. Agent-Based models? Nope, not differentiable... or are they? Check out our new paper at NeurIPS on Stochastic dP!🧵

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Moritz Schauer

@MoritzSchauer

3 years

@ss2520_2nd Overflow?

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Moritz Schauer

@MoritzSchauer

8 months

@adad8m Should be exactly these basis functions I think one could compare

Kosambi–Karhunen–Loève theorem - Wikipedia

en.wikipedia.org

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Moritz Schauer

@MoritzSchauer

1 year

@rlmcelreath 10 great ideas how to get more stats out of your MS Paint: 1. Regression and Nonparametric regression 1/10

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Moritz Schauer

@MoritzSchauer

8 months

Let's see how to answer this with CausalInference.jl

Ryan Travis

@ryan_ttest

8 months

Need some causal inference help. If I have the following graph, how do I estimate the effect of T on O while removing the effect of T -> P -> O? Appreciate any help!

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Moritz Schauer

@MoritzSchauer

3 years

I made a @PlutoJL notebook: Interactive tour on non-parametric Bayesian regression using #julialang . If you ever wanted to play visually with posterior contraction rates...

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Moritz Schauer

@MoritzSchauer

2 years

@MaartenvSmeden On 99 you see the “Polish Matura exam rounding effect” (Distribution of results of the Matura exam in Poland in 2013. The minimum score to pass is 30%.)

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Moritz Schauer

@MoritzSchauer

5 months

@oxinabox_frames

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Moritz Schauer

@MoritzSchauer

6 months

It's our responsibility to sometimes retweet this blog post on the worst estimator of the universe

The Harmonic Mean of the Likelihood: Worst Monte Carlo Method Ever

Many Bayesian statisticians decide which of several models is most appropriate for a given dataset by computing the marginal likelihood of each model (also called the integrated likelihood or the e…

radfordneal.wordpress.com

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Moritz Schauer

@MoritzSchauer

8 months

Yeah, I use curl -LH "Accept: application/x-bibtex" -w "\n" $(< dois.txt) > doi.bib to generate my bib file from a list of doi's.

Richard McElreath 🦔

@rlmcelreath

8 months

Do you like bibtex? Do you doi? Do you want to get bibtex refs from doi on the command line? Yes you do, you wonderful monster. Try this line (adjust doi as needed): curl -LH "Accept: application/x-bibtex"

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Moritz Schauer

@MoritzSchauer

3 years

@thienan496 Yeah, that the Karhunen–Loève

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Moritz Schauer

@MoritzSchauer

2 years

@dittrich_lars Das macht mir schon Sorgen, vor allem wenn Jugendliche für den "Kick" absichtlich eine potentiell gefährliche Unterdosis durch verdünnen und schütteln herbeiführen.

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Moritz Schauer

@MoritzSchauer

3 years

@tjmahr @rlmcelreath @jvcasill I like the converse: if we don’t get the prior back we have learned something

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Moritz Schauer

@MoritzSchauer

6 months

When are Unbiased Monte Carlo Estimators More Preferable than Biased Ones? Guanyang Wang, Jose Blanchet, Peter W.Glynn

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Moritz Schauer

@MoritzSchauer

6 years

A blog post in which @GugushviliShota and I explain how to use our #julialang package "MicrostructureNoise" for Bayesian nonparametric volatility estimation

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Moritz Schauer

@MoritzSchauer

1 year

About continuity and measurability… Continuity starts with informal notion of drawing a line without lifting the pen. From the formal definition, continuity looks like a property of pre-images f⁻¹(B) , but the informal notion seems like a property of f. How that? (1/n)

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Moritz Schauer

@MoritzSchauer

4 years

Let's do a beautiful #science #randomwalk It starts at a lake and in a moment raindrops will fall making little ripples

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Moritz Schauer

@MoritzSchauer

1 year

@JDHamkins Fold into a cylinder using muffin cup folds and flatten the cylinder: half the circumference of the hole.

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Moritz Schauer

@MoritzSchauer

4 years

New on arXiv: "Automatic Backward Filtering Forward Guiding for Markov processes and graphical models" with Frank van der Meulen, : how to do continuous time Markov processes as building blocks in probabilistic graphical models... automatically

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Moritz Schauer

@MoritzSchauer

1 year

"Bernoulli experiment" for a coin flip is a high contender.

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Moritz Schauer

@MoritzSchauer

1 year

Announcing CausalInference.jl 0.11 with greedy equivalence search and Dagitty-like adjustment set search #causalinference #julialang

ANN:CausalInference.jl - Causal Inference in Julia

ANN: Causal Inference 0.11.1 Just in time for JuliaCon we have added with the help of @RobertGregg the Parallel Greedy Equivalence Search (GES) as score based alternative to the PC algorithm! Marcel...

discourse.julialang.org

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Moritz Schauer

@MoritzSchauer

5 years

Marcin Mider, Moritz Schauer, Frank van der Meulen: Continuous-discrete smoothing of diffusions. The theory for #julialang package #DataAssimilation

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Moritz Schauer

@MoritzSchauer

3 years

My #JuliaCon talk on ZigZagBoomerang.jl - variable selection and public release of parallel sampling with the zigzag #pdmp

ZigZagBoomerang.jl - parallel inference and variable selection |...

This talk was given as part of JuliaCon2021.Abstract:ZigZagBoomerang.jl provides piecewise deterministic Monte Carlo methods. They have the same goal as clas...

www.youtube.com

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Moritz Schauer

@MoritzSchauer

7 months

Ah, this is related to the efficient way of getting a Brownian bridge by subtracting tW₁ from a Brownian motion Wₜ (because Cov(Wₜ, W₁) = min(t, 1) = t for t ∈ [0, 1].)

Alexander Terenin

@avt_im

3 years

Our recently-accepted JMLR paper "Pathwise Conditioning of Gaussian Processes" is now live! Check it out! @mpd37

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Moritz Schauer

@MoritzSchauer

7 months

@Quasilocal Short shot:

math prof

@mathematicsprof

6 years

@DavidFeldman

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Moritz Schauer

@MoritzSchauer

2 years

I'll be speaking next Tuesday 18:00-19:00 UTC+1 at the seminar on "Bidirectional compositionality in inference and stochastic optimisation"

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Moritz Schauer

@MoritzSchauer

2 years

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Moritz Schauer

@MoritzSchauer

2 years

🎉Dr. Sebastiano Grazzi! 🎉 @SebastianoGraz3

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Moritz Schauer

@MoritzSchauer

7 months

Famous last words: It’s a discrete space with finitely many elements, how hard can it be?

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Moritz Schauer

@MoritzSchauer

3 years

Blog: Frank Schäfer - Neural Hybrid Differential Equations Google Summer of Code project #gsoc #JuliaLang

Neural Hybrid Differential Equations | FS

I am delighted that I have been awarded my second GSoC stipend this year. I look forward to carrying out the ambitious project scope with my mentors Chris Rackauckas, Moritz Schauer, Yingbo Ma, and...

frankschae.github.io

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Moritz Schauer

@MoritzSchauer

4 years

High weak order SDE solvers

High weak order SDE solvers | FS

This post summarizes our new high weak order methods for the SciML ecosystem, as implemented within the Google Summer of Code 2020 project. After an introductory part highlighting the differences...

frankschae.github.io

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Moritz Schauer

@MoritzSchauer

5 months

Uh, X ~ Poisson(λ) conditioned on X > k doesn't have a name and is not found on wikipedia. That's a first.

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Moritz Schauer

@MoritzSchauer

1 year

Julia code at

GitHub - gaurav-arya/differentiable_mh: Code for paper https://arxiv.org/abs/2306.07961

Code for paper https://arxiv.org/abs/2306.07961. Contribute to gaurav-arya/differentiable_mh development by creating an account on GitHub.

github.com

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Moritz Schauer

@MoritzSchauer

5 years

Open PhD position(s) in applied mathematics for neural networks and AI. See for my project at the intersection of statistics, machine learning and stochastic analysis. @ChalmersAI

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Moritz Schauer

@MoritzSchauer

7 months

@adad8m If you take rubber bands (which pull with approximately quadratic force by Hooke’s law) it does minimise the sum of squared residuals. I use this in my lecture

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Moritz Schauer

@MoritzSchauer

4 years

Such as: implement algorithms for counterfactual ("what if") reasoning and causal analysis to #Fairness .jl with @acidflask @ZennaTavares , Sebastian Vollmer and me

The Julia Language

@JuliaLanguage

4 years

We are excited to announce we have been selected as a mentoring organization for GSoC ‘21: Know any students who would be interested in spending a summer doing #JuliaLang work? Send them out way! #OpenSource #CodeNewbies #AnyoneCanCode

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Moritz Schauer

@MoritzSchauer

7 years

#julialang @MathieuBesancon I picked up your blog post and wrote a Julia notebook on parameter inference for the SIR model

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Moritz Schauer

@MoritzSchauer

2 years

@ChrisRackauckas Demo

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Moritz Schauer

@MoritzSchauer

5 years

New preprint: Alexis Arnaudon, Frank van der Meulen, Moritz Schauer, Stefan Sommer: Diffusion bridges for stochastic Hamiltonian systems with applications to shape analysis. #Julialang package: @arnaudon

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Moritz Schauer

@MoritzSchauer

2 years

Today "Applied Measure Theory for Composable Statistical Modeling" by @ChadScherrer at @ToposInstitute colloquium (see link for time)

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Moritz Schauer

@MoritzSchauer

4 years

New paper on arXiv "Sticky PDMP samplers for sparse and local inference problems" by @jbierkens @SebastianoGraz3 @MeulenFrank and me.

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Moritz Schauer

@MoritzSchauer

3 years

@sam_power_825 Any other upper bound

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Moritz Schauer

@MoritzSchauer

4 years

Great outcome of the @JuliaLanguage Google summer of code projects - looking at all these blog post really shows the scope

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Moritz Schauer

@MoritzSchauer

2 years

A quasi-Gaussian golden sunflower

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Moritz Schauer

@MoritzSchauer

8 months

The first (uniform) image shows a Brownian bridge by the ❤️. The others are essentially distorted Brownian bridges. One can even use the limiting distribution to derive confidence sets.

A New Approach to Tests and Confidence Bands for Distribution Functions

We introduce new goodness-of-fit tests and corresponding confidence bands for distribution functions. They are inspired by multi-scale methods of testing and based on refined laws of the iterated...

arxiv.org

Seth Axen 🪓

@sethaxen

8 months

Working on adding some confidence bands to my ECDFs and wrote up some notes/experiments

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Moritz Schauer

@MoritzSchauer

1 year

@Hassaan_PHY Eiger is steigerungsform/comparative. Hence eigervalues are values that are more eigen than eigenvalues.

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Moritz Schauer

@MoritzSchauer

1 year

⁦ @NotGauravArya ⁩ about StochasticAD.jl at #JuliaCon . #differentiatealmosteverything

StochasticAD.jl: Differentiating Discrete Randomness | Gaurav Arya |...

Automatic differentiation (AD) is great: use gradients to optimize, sample faster, or just for fun! But what about coin flips? Agent-based models? Nope, thes...

www.youtube.com

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Moritz Schauer

@MoritzSchauer

3 years

( @JohannesTextor ) is nice: DAGitty is a browser-based environment for creating, editing, and analyzing causal diagrams (directed acyclic graphs or causal Bayesian networks)

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Moritz Schauer

@MoritzSchauer

1 year

Which mathematicians have the most mundane concepts named after them?

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Moritz Schauer

@MoritzSchauer

7 months

@pastramimachine Let’s play “Halo Level or Campus?”

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Moritz Schauer

@MoritzSchauer

3 years

Oh, this does not look good: people deserve reliable wikipedia entries about such fundamental concepts.

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Moritz Schauer

@MoritzSchauer

2 years

@mattansb A number X is drawn from U([-2, 2]) and I observe that |X| > 1 (but not X), then I gain uncertainty: variance of the conditional distribution goes up from 4/3 to 7/3.

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Moritz Schauer

@MoritzSchauer

1 year

If you know the Rosenbrock function from optimisation, maybe you have not seen this nice interpretation. Draw X ~ N(a, ½), then Y ∼ N(X², (2b)⁻¹). The joint log-density of (X,Y) is f(x) = -(a - x)² - b(y - x²)² (Image: CC BY-SA 4.0 Wikipedia User Nschloe)

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Moritz Schauer

@MoritzSchauer

1 year

That allows us to create efficient gradient estimates of Metropolis Hastings samplers using StochasticAD

Dr. Chris Rackauckas

@ChrisRackauckas

2 years

Differentiable programming (dP) is great: train neural networks to match anything w/ gradients! ODEs? Neural ODEs. Physics? Yes. Agent-Based models? Nope, not differentiable... or are they? Check out our new paper at NeurIPS on Stochastic dP!🧵

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Moritz Schauer

@MoritzSchauer

6 months

Particle sampler without resampling

Anders Eklund

@wandedob

6 months

1 ball = 1 grant application

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Moritz Schauer

@MoritzSchauer

1 year

Let's resurrect the term "inversion"? Classically, having a prior on X and a forward model giving the conditional probability of observing Y given X, we ask for X given Y. I like the perspective of changing the direction of information flow (from X → Y to Y → X). I

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Moritz Schauer

@MoritzSchauer

3 years

Ref. Frank Schäfer's @gsoc project on Sensitivity Analysis of Hybrid Differential Equations () with implicit events for the SciML ecosystem #julialang

Sensitivity Analysis of Hybrid Differential Equations | FS

In this post, we discuss sensitivity analysis of differential equations with state changes caused by events triggered at defined moments, for example reflections, bounces off a wall or other sudden...

frankschae.github.io

\mathfrak{Michael "Shapes Dude" Betancourt}

@betanalpha

3 years

New paper alert! In this paper Charles Margossian and I attempt a unified framework for incorporating implicit functions into automatic differentiation, .

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Moritz Schauer

@MoritzSchauer

1 year

Measurable maps are those that don’t separate sets that touch! Here sets A and B touch (are proximal) in 𝒜 if there is no S ∈ 𝒜 such that A ⊂ S and B ⊂ Sᶜ.

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Moritz Schauer

@MoritzSchauer

2 years

@ylecun @Jake_Browning00 I’d be already happy if people understood that mental verbalization is mostly the shadow, not the thing

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Moritz Schauer

@MoritzSchauer

1 year

Do you know any distribution on [0, ∞) where the mean equals the median?

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Moritz Schauer

@MoritzSchauer

1 year

@tunguz Taking the bait...

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Moritz Schauer

@MoritzSchauer

1 year

MH samplers are not traditionally differentiable due to the discrete accept/reject steps for proposed samples. A perturbation of the target can cause the original chain and the perturbed chain to diverge if they happen to accept/reject differently.

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Moritz Schauer

@MoritzSchauer

1 year

@adad8m Unbiasedness allows to average many noisy estimates. Think of the scenario where you measure sample in small groups with different mean but common variance and then want to accumulate results to estimate global variance.

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Moritz Schauer

@MoritzSchauer

7 months

@sp_monte_carlo With @betanalpha : statistically meaningful quantities like posterior means and posterior variance are integrals, so even if you have the posterior density you still need to integrate. Samples solve the integration problem.

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Moritz Schauer

@MoritzSchauer

5 years

Interested in a PhD working in #julialang on a simulator of the impact of climate change on all plant biodiversity on earth?

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Moritz Schauer

@MoritzSchauer

1 year

The key is to couple both chains, but common random numbers are not enough. With a good coupling, the perturbed chain deviates from the original chain only by short excursions.

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Moritz Schauer

@MoritzSchauer

9 months

Nice, all Banach-Tarski jokes in a single tweet.

Almost Sure

@Almost_Sure

9 months

did you know: starting from a single tweet about Banach-Tarski, it is possible to dissect it and create 100 new Banach-Tarski tweets

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Moritz Schauer

@MoritzSchauer

2 years

It is just a function with many parameters.

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Moritz Schauer

@MoritzSchauer

1 year

We illustrate this with maximizing the specific heat in an Ising model by differentiating through Metropolis Hastings. The image illustrates how a chain with a infinitesimally perturbed temperature in the Ising model deviates for some iterations before merging again.

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Moritz Schauer

@MoritzSchauer

3 years

@ChadScherrer @AllenDowney Love it!

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Moritz Schauer

@MoritzSchauer

1 year

Methodologically reassuring that a single math department (ours, the joint math department of Chalmers University and of the University of Gothenburg) ranks simultaneously second best and worst of Swedish math departments. (Thanks Axel!)

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Moritz Schauer

@MoritzSchauer

2 years

To my mind digits face to the left 1 2 3 4 5… and most letters to the right A B C D E F G…

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Moritz Schauer

@MoritzSchauer

1 year

A PhD: find a very specific solution to a problem others overlooked by extending general theory

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Moritz Schauer

@MoritzSchauer

8 months

The grid lines on graph paper are prison bars for the mind

Anthony Bonato

@Anthony_Bonato

8 months

Math on blank paper, grid paper, or lined paper?

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Moritz Schauer

@MoritzSchauer

6 months

"to Polish"

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Moritz Schauer

@MoritzSchauer

1 year

Got asked on the way to Kindergarten if one can count not only forward or backward, but also sideways. Love the implication: 1, 1 + i, 1 + 2i, …

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Moritz Schauer

@MoritzSchauer

3 years

@ChrisRackauckas @cameron_pfiffer @JuliaLanguage I have a small collection of interoperability gems at

Package interoperability showcases

Four-way 🙂 using Turing, Distributions, IntervalArithmetic, ForwardDiff @model model() = begin X ~ Normal() end v = Turing.VarInfo(model()) sampler = Turing.SampleFromPrior() ctx = DynamicPPL.Defa...

discourse.julialang.org

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Moritz Schauer

@MoritzSchauer

1 year

So it turns out that Greedy Causal Discovery which greedily adds (phase 1) and then removes (phase 2) edges from equivalence classes of causal graphs and yet finds an optimum is a form of simplex algorithm

Greedy Causal Discovery Is Geometric | SIAM Journal on Discrete Mathematics

Abstract. Finding a directed acyclic graph (DAG) that best encodes the conditional independence statements observable from data is a central question within causality. Algorithms that greedily...

epubs.siam.org

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Moritz Schauer

@MoritzSchauer

8 months

As the statisticians say: you fail to miss 5% of the chances you should not have taken!

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Moritz Schauer

@MoritzSchauer

3 years

My @ISBA_events talk about "Sticky piecewise deterministic Markov samplers for inference problems with spike and slab priors"

Moritz Schauer: Sticky piecewise deterministic Monte Carlo samplers...

Arxiv: https://arxiv.org/abs/2103.08478We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov proc...

www.youtube.com

Moritz Schauer

@MoritzSchauer

4 years

New paper on arXiv "Sticky PDMP samplers for sparse and local inference problems" by @jbierkens @SebastianoGraz3 @MeulenFrank and me.

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Moritz Schauer

@MoritzSchauer

1 year

Shout-out to first authors @NotGauravArya and Ruben Seyer (first paper!) soon starting as PhD

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Moritz Schauer

@MoritzSchauer

11 months

Take an undirected cycle graph, and orient the edges by coin flip. What is the distribution of sinks? Hint: zero is a special case of an even.

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Moritz Schauer

@MoritzSchauer

1 year

One more: The Kronecker-δ, a function that returns 1 if two indices are equal and 0 otherwise

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Moritz Schauer

@MoritzSchauer

5 years

New preprint: Joris Bierkens, Sebastiano Grazzi (first paper!), Frank van der Meulen, M.S.: A piecewise deterministic Monte Carlo method for diffusion bridges

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Moritz Schauer

@MoritzSchauer

3 years

There is a nice connection between Gamma process and spatial Poisson process: The little and larger jumps ΔXₜ of a Gamma process Xₜ plotted in the (t, log(Δx)) plane form a Poisson point process, increasingly homogeneous for small Δx @genkuroki

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Moritz Schauer

@MoritzSchauer

2 years

@ShengwuLi Lol, ChatGPT is probably trained on that sentence

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Moritz Schauer

@MoritzSchauer

6 years

@wuoulf @SimonDanisch @graalvm @JuliaLanguage @usenextjournal This is really @usenextjournal working as supposed: someone remixes an article, reproduces the results and adds a new angle to it. 🧡

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Moritz Schauer

@MoritzSchauer

2 years

@rlmcelreath 20 minutes on a TikZ diagram - is this a brag?

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Moritz Schauer

@MoritzSchauer

3 years

Ad: Laplace Demon Webinar: @MeulenFrank - Automatic Backward Filtering Forward Guiding for Markov processes and graphical models

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Moritz Schauer

@MoritzSchauer

2 years

Σ is a covariance and σ a scale - Λ is a Laplacian and λ a rate... that's actually quite nice

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Moritz Schauer

@MoritzSchauer

3 years

PS: Package announcement on the #julialang discourse forum:

[ANN] ZigZagBoomerang.jl

Dear all! We would like to announce our package together with our new paper “Sticky PDMP samplers for sparse and local inference problems” (Arxiv link) ZigZagBoomerang.jl Sleek implementations of the...

discourse.julialang.org

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Moritz Schauer

@MoritzSchauer

11 months

Terence Tao looking into automatic theorem proving is a nice signal. This playful environment by @XenaProject and Mohammad Pedramfar of learning the theorem prover Lean is great

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Moritz Schauer

@MoritzSchauer

1 year

@adad8m I feel seen in the continuous education cycle

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Moritz Schauer

@MoritzSchauer

3 years

@avehtari This interactive notebook is perhaps close to the case @avehtari has in mind: A Gaussian process prior using the Fourier basis (n observations, n basis functions) in a regression context

Moritz Schauer

@MoritzSchauer

3 years

I made a @PlutoJL notebook: Interactive tour on non-parametric Bayesian regression using #julialang . If you ever wanted to play visually with posterior contraction rates...

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Moritz Schauer

@MoritzSchauer

3 years

@ChadScherrer @sp_monte_carlo This one I just saw recently

Keenan Crane

@keenanisalive

3 years

Anyone know a good article on how complex numbers improve robustness of numerical & geometric computation? E.g., sqrt(-ε) is NaN in real arithmetic, but sqrt(ε)i in complex arithmetic. Also, two circles have a complex intersection—even if they don’t quite touch due to rounding.

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