youtube links to the transformer video that is helpful for
understanding the transformer:
https://www.youtube.com/watch?v=wjZofJX0v4M
https://www.youtube.com/watch?v=eMlx5fFNoYc
3Blue1Brown. (2024, April 1). Transformers, the tech behind LLMs | Deep Learning Chapter 5 [Video]. YouTube.
https://www.youtube.com/watch?v=wjZofJX0v4M
Attention in transformers, step-by-step | Deep Learning Chapter 6
Ganegedara, T. (2025, February 2). Intuitive Guide to Latent Dirichlet Allocation. Towards Data Science.
https://towardsdatascience.com/light-on-math-machine-learning-intuitive-guide-to-latent-dirichlet-allocation-437c81220158/
some blogs
https://johaupt.github.io/blog/Topic_modeling_with_Gibbs_sampling_in_R.html https://agustinus.kristia.de/blog/lda-gibbs/
See Box 1, viz:
QT:{{”
Box 1 Statistical model used in the GREML approach to estimate hS2NP The statistical model used by GREML can be described in its simplest form as y = Wu + e
where y is an n x 1 vector of standardized phenotypes with n equal to the sample size, W = {wij} is an n x m standardized SNP genotype matrix where m is the number of SNPs, u = {ui} is an m x 1 vector of the additive effects of all variants when fitted jointly in the model, u ~ N(0,Iσ2) with I being an identity matrix, u and e is a vector of residuals, e ~ N(0,Iσ2). An equivalent model is….
y=g+e
g ~ N(0,A…)
A=W W’
In practice, A is called the SNP-derived genetic (or genomic) relationship matrix (GRM) and is estimated from the SNP data. The estimate …from GREML can be described as the estimated variance explained by all the SNPs (mσu) or equivalently as the estimated genetic variance by contrasting the phenotypic similarity
between unrelated individuals to their SNP-derived genetic similarity “}}
https://www.nature.com/articles/ng.3941
Yang, J., Zeng, J., Goddard, M. E., Wray, N. R., & Visscher, P. M. (2017). Concepts, estimation and interpretation of SNP-based heritability. Nature Genetics, 49(9), 1304–1310.
https://doi.org/10.1038/ng.3941
http://mcb111.org/w06/w06-lecture.html
Has some nice textbook downloads – e.g.
http://mcb111.org/w06/KollerFriedman.pdf
QT:{{”
There are many good books to learn about probabilistic models. “Probabilistic graphical models: principles and techniques” (by Koller & Friedman) is a comprehensive source about more general probabilistic models than the one we are going to study here.
“}}
Subset of chap 7 focuses on GMRF
good tutorial/textbook chaper/review paper on Poisson regression :
Below are a few readings that discuss how to fit a generalized linear mixed model.
1. Breslow & Clayton (1993), JASA, Approximate Inference in
Generalized Linear Mixed Models.
https://doi.org/10.2307/2290687
A classic statistical paper introducing the Laplace approximation and penalized quasi-likelihood for GLMMs
2. Bates (2011), Mixed models in R using the lme4 package Part 5: Generalized linear mixed models
https://lme4.r-forge.r-project.org/slides/2011-03-16-Amsterdam/5GLMMH.pdf 3. Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of statistical software, 67, 1-48.
https://doi.org/10.18637/jss.v067.i01
4. Bates (2025), Computational methods for mixed models
https://cran.r-project.org/web/packages/lme4/vignettes/Theory.pdf
These are written by the authors of the lme4 package, discussing the details of how a mixed-effects model (more specifically, a generalized linear mixed-effects model) is trained using the PIRLS approach.
1. Paulsson (2005) – “Models of stochastic gene expression”
https://www.sciencedirect.com/science/article/abs/pii/S1571064505000138 Nice pedagogical review of the master equation framework – covers the conceptual foundations and different analytical approaches.
2. Shahrezaei & Swain (2008) – “Analytical distributions for stochastic gene expression”
https://pubmed.ncbi.nlm.nih.gov/18988743/
This one derives the exact analytical solutions to the master equation for protein/mRNA distributions.
The Paulsson paper is probably better as a tutorial.
However, it’s a bit difficult to connect to protein & mRNA.
some reading materials on RL:
https://arxiv.org/pdf/2412.05265
https://arxiv.org/abs/2412.05265
Murphy, K. (2024, December 6). Reinforcement Learning: An Overview. arXiv.org. https://arxiv.org/abs/2412.05265
QT:{{”
Reinforcement learning or RL is a class of methods for solving various kinds of sequential decision making
tasks. In such tasks, we want to design an agent that interacts with an external environment. The agent
maintains an internal state zt, which it passes to its policy π to choose an action at = π(zt). The environment
responds by sending back an observation ot+1, which the agent uses to update its internal state using the
state-update function zt+1 = SU(zt, at, ot+1). See Figure 1.1 for an illustration.
To simplify things, we often assume that the environment is also a Markovian process, which has internal
world state wt, from which the observations ot are derived. (This is called a POMDP — see Section 1.2.1).
We often simplify things even more by assuming that the observation ot reveals the hidden environment state;
in this case, we denote the internal agent state and external environment state by the same letter, namely
st = ot = wt = zt. (This is called an MDP — see Section 1.2.2). We discuss these assumptions in more detail
in Section 1.1.3.
RL is more complicated than supervised learning (e.g., training a classifier) or self-supervised learning
(e.g., training a language model), because this framework is very general: there are many assumptions we can
make about the environment and its observations ot, and many choices we can make about the form the
agent’s internal state zt and policy π, as well the ways to update these objects as we see more data. We
will study many different combinations in the rest of this document. The right choice ultimately depends on
which real-world application you are interested in solving.1 .”}}
some tutorials on flow-matching:
https://arxiv.org/pdf/2412.06264
https://arxiv.org/pdf/2506.02070
Lipman, Y., Havasi, M., Holderrieth, P., Shaul, N., Le, M., Karrer, B., Chen, R. T. Q., Lopez-Paz, D., Ben-Hamu, H., & Gat, I. (2024, December 9). Flow matching guide and code. arXiv.org.
https://arxiv.org/abs/2412.06264
(Sometimes difficult to follow formalism)
Holderrieth, P., & Erives, E. (2025). MIT Class 6.S184: Generative AI with Stochastic Differential equations (pp. 1–52).
https://arxiv.org/pdf/2506.02070
OR
Holderrieth, P., & Erives, E. (2025, June 2). An introduction to flow matching and diffusion models. arXiv.org.
https://arxiv.org/abs/2506.02070
(Very intuitive!!!)
linkstream2 microblog 