Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.
Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.
Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from an “amateur mathematician and computer scientist” standpoint.
Why is it hard to approach?
Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
@@ -135,7 +148,21 @@
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ICLR is one of the most important conferences in machine learning, and as such, I was very excited to have the opportunity to volunteer and attend the first fully-virtual edition of the event. The whole content of the conference has been made publicly available, only a few days after the end of the event!
ICLR is one of the most important conferences in machine learning, and as such, I was very excited to have the opportunity to volunteer and attend the first fully-virtual edition of the event. The whole content of the conference has been made publicly available, only a few days after the end of the event!
I would like to thank the organizing committee for this incredible event, and the possibility to volunteer to help other participantsTo better organize the event, and help people navigate the various online tools, they brought in 500(!) volunteers, waved our registration fees, and asked us to do simple load-testing and tech support. This was a very generous offer, and felt very rewarding for us, as we could attend the conference, and give back to the organization a little bit.
.
@@ -191,7 +218,15 @@
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Two weeks ago, I did a presentation for my colleagues of the paper from Yurochkin et al. (2019), from NeurIPS 2019. It contains an interesting approach to document classification leading to strong performance, and, most importantly, excellent interpretability.
Two weeks ago, I did a presentation for my colleagues of the paper from Yurochkin et al. (2019), from NeurIPS 2019. It contains an interesting approach to document classification leading to strong performance, and, most importantly, excellent interpretability.
This paper seems interesting to me because of it uses two methods with strong theoretical guarantees: optimal transport and topic modelling. Optimal transport looks very promising to me in NLP, and has seen a lot of interest in recent years due to advances in approximation algorithms, such as entropy regularisation. It is also quite refreshing to see approaches using solid results in optimisation, compared to purely experimental deep learning methods.
Introduction and motivation
The problem of the paper is to measure similarity (i.e. a distance) between pairs of documents, by incorporating semantic similarities (and not only syntactic artefacts), without encountering scalability issues.
I have recently bought the book Category Theory from Steve Awodey (Awodey 2010) is awesome, but probably the topic for another post), and a particular passage excited my curiosity:
Let us begin by distinguishing between the following things: i. categorical foundations for mathematics, ii. mathematical foundations for category theory.
@@ -524,7 +570,15 @@ then \(\varphi(n)\) is true for every natural n
I recently got interested in APL, an array-based programming language. In APL (and derivatives), we try to reason about programs as series of transformations of multi-dimensional arrays. This is exactly the kind of style I like in Haskell and other functional languages, where I also try to use higher-order functions (map, fold, etc) on lists or arrays. A developer only needs to understand these abstractions once, instead of deconstructing each loop or each recursive function encountered in a program.
APL also tries to be a really simple and terse language. This combined with strange Unicode characters for primitive functions and operators, gives it a reputation of unreadability. However, there is only a small number of functions to learn, and you get used really quickly to read them and understand what they do. Some combinations also occur so frequently that you can recognize them instantly (APL programmers call them idioms).
@@ -730,7 +784,13 @@ then \(\varphi(n)\) is true for every natural n
-
The Ising model is a model used to represent magnetic dipole moments in statistical physics. Physical details are on the Wikipedia page, but what is interesting is that it follows a complex probability distribution on a lattice, where each site can take the value +1 or -1.
The Ising model is a model used to represent magnetic dipole moments in statistical physics. Physical details are on the Wikipedia page, but what is interesting is that it follows a complex probability distribution on a lattice, where each site can take the value +1 or -1.
Mathematical definition
We have a lattice \(\Lambda\) consisting of sites \(k\). For each site, there is a moment \(\sigma_k \in \{ -1, +1 \}\). \(\sigma =
@@ -850,7 +910,23 @@ J\sigma_i \sum_{j\sim i} \sigma_j. \]
-
L-systems are a formal way to make interesting visualisations. You can use them to model a wide variety of objects: space-filling curves, fractals, biological systems, tilings, etc.
L-systems are a formal way to make interesting visualisations. You can use them to model a wide variety of objects: space-filling curves, fractals, biological systems, tilings, etc.
Two weeks ago, I did a presentation for my colleagues of the paper from Yurochkin et al. (2019), from NeurIPS 2019. It contains an interesting approach to document classification leading to strong performance, and, most importantly, excellent interpretability.
Two weeks ago, I did a presentation for my colleagues of the paper from Yurochkin et al. (2019), from NeurIPS 2019. It contains an interesting approach to document classification leading to strong performance, and, most importantly, excellent interpretability.
This paper seems interesting to me because of it uses two methods with strong theoretical guarantees: optimal transport and topic modelling. Optimal transport looks very promising to me in NLP, and has seen a lot of interest in recent years due to advances in approximation algorithms, such as entropy regularisation. It is also quite refreshing to see approaches using solid results in optimisation, compared to purely experimental deep learning methods.
Introduction and motivation
The problem of the paper is to measure similarity (i.e. a distance) between pairs of documents, by incorporating semantic similarities (and not only syntactic artefacts), without encountering scalability issues.
ICLR is one of the most important conferences in machine learning, and as such, I was very excited to have the opportunity to volunteer and attend the first fully-virtual edition of the event. The whole content of the conference has been made publicly available, only a few days after the end of the event!
ICLR is one of the most important conferences in machine learning, and as such, I was very excited to have the opportunity to volunteer and attend the first fully-virtual edition of the event. The whole content of the conference has been made publicly available, only a few days after the end of the event!
I would like to thank the organizing committee for this incredible event, and the possibility to volunteer to help other participantsTo better organize the event, and help people navigate the various online tools, they brought in 500(!) volunteers, waved our registration fees, and asked us to do simple load-testing and tech support. This was a very generous offer, and felt very rewarding for us, as we could attend the conference, and give back to the organization a little bit.
I recently got interested in APL, an array-based programming language. In APL (and derivatives), we try to reason about programs as series of transformations of multi-dimensional arrays. This is exactly the kind of style I like in Haskell and other functional languages, where I also try to use higher-order functions (map, fold, etc) on lists or arrays. A developer only needs to understand these abstractions once, instead of deconstructing each loop or each recursive function encountered in a program.
APL also tries to be a really simple and terse language. This combined with strange Unicode characters for primitive functions and operators, gives it a reputation of unreadability. However, there is only a small number of functions to learn, and you get used really quickly to read them and understand what they do. Some combinations also occur so frequently that you can recognize them instantly (APL programmers call them idioms).
The Ising model is a model used to represent magnetic dipole moments in statistical physics. Physical details are on the Wikipedia page, but what is interesting is that it follows a complex probability distribution on a lattice, where each site can take the value +1 or -1.
The Ising model is a model used to represent magnetic dipole moments in statistical physics. Physical details are on the Wikipedia page, but what is interesting is that it follows a complex probability distribution on a lattice, where each site can take the value +1 or -1.
Mathematical definition
We have a lattice \(\Lambda\) consisting of sites \(k\). For each site, there is a moment \(\sigma_k \in \{ -1, +1 \}\). \(\sigma =
diff --git a/_site/posts/lsystems.html b/_site/posts/lsystems.html
index 04f3702..05ba0e0 100644
--- a/_site/posts/lsystems.html
+++ b/_site/posts/lsystems.html
@@ -54,7 +54,23 @@
-
L-systems are a formal way to make interesting visualisations. You can use them to model a wide variety of objects: space-filling curves, fractals, biological systems, tilings, etc.
L-systems are a formal way to make interesting visualisations. You can use them to model a wide variety of objects: space-filling curves, fractals, biological systems, tilings, etc.
Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.
Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.
Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from an “amateur mathematician and computer scientist” standpoint.
Why is it hard to approach?
Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
diff --git a/_site/posts/peano.html b/_site/posts/peano.html
index bda02d7..7aa3903 100644
--- a/_site/posts/peano.html
+++ b/_site/posts/peano.html
@@ -52,7 +52,18 @@
I have recently bought the book Category Theory from Steve Awodey (Awodey 2010) is awesome, but probably the topic for another post), and a particular passage excited my curiosity:
Let us begin by distinguishing between the following things: i. categorical foundations for mathematics, ii. mathematical foundations for category theory.
Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.
Operations research (OR) is a vast area comprising a lot of theory, different branches of mathematics, and too many applications to count. In this post, I will try to explain why it can be a little disconcerting to explore at first, and how to start investigating the topic with a few references to get started.
Keep in mind that although I studied it during my graduate studies, this is not my primary area of expertise (I’m a data scientist by trade), and I definitely don’t pretend to know everything in OR. This is a field too vast for any single person to understand in its entirety, and I talk mostly from an “amateur mathematician and computer scientist” standpoint.
Why is it hard to approach?
Operations research can be difficult to approach, since there are many references and subfields. Compared to machine learning for instance, OR has a slightly longer history (going back to the 17th century, for example with Monge and the optimal transport problem) For a very nice introduction (in French) to optimal transport, see these blog posts by Gabriel Peyré, on the CNRS maths blog: Part 1 and Part 2. See also the resources on optimaltransport.github.io (in English).
@@ -131,7 +144,21 @@
-
ICLR is one of the most important conferences in machine learning, and as such, I was very excited to have the opportunity to volunteer and attend the first fully-virtual edition of the event. The whole content of the conference has been made publicly available, only a few days after the end of the event!
ICLR is one of the most important conferences in machine learning, and as such, I was very excited to have the opportunity to volunteer and attend the first fully-virtual edition of the event. The whole content of the conference has been made publicly available, only a few days after the end of the event!
I would like to thank the organizing committee for this incredible event, and the possibility to volunteer to help other participantsTo better organize the event, and help people navigate the various online tools, they brought in 500(!) volunteers, waved our registration fees, and asked us to do simple load-testing and tech support. This was a very generous offer, and felt very rewarding for us, as we could attend the conference, and give back to the organization a little bit.
.
@@ -187,7 +214,15 @@
-
Two weeks ago, I did a presentation for my colleagues of the paper from Yurochkin et al. (2019), from NeurIPS 2019. It contains an interesting approach to document classification leading to strong performance, and, most importantly, excellent interpretability.
Two weeks ago, I did a presentation for my colleagues of the paper from Yurochkin et al. (2019), from NeurIPS 2019. It contains an interesting approach to document classification leading to strong performance, and, most importantly, excellent interpretability.
This paper seems interesting to me because of it uses two methods with strong theoretical guarantees: optimal transport and topic modelling. Optimal transport looks very promising to me in NLP, and has seen a lot of interest in recent years due to advances in approximation algorithms, such as entropy regularisation. It is also quite refreshing to see approaches using solid results in optimisation, compared to purely experimental deep learning methods.
Introduction and motivation
The problem of the paper is to measure similarity (i.e. a distance) between pairs of documents, by incorporating semantic similarities (and not only syntactic artefacts), without encountering scalability issues.
I have recently bought the book Category Theory from Steve Awodey (Awodey 2010) is awesome, but probably the topic for another post), and a particular passage excited my curiosity:
Let us begin by distinguishing between the following things: i. categorical foundations for mathematics, ii. mathematical foundations for category theory.
@@ -520,7 +566,15 @@ then \(\varphi(n)\) is true for every natural n
I recently got interested in APL, an array-based programming language. In APL (and derivatives), we try to reason about programs as series of transformations of multi-dimensional arrays. This is exactly the kind of style I like in Haskell and other functional languages, where I also try to use higher-order functions (map, fold, etc) on lists or arrays. A developer only needs to understand these abstractions once, instead of deconstructing each loop or each recursive function encountered in a program.
APL also tries to be a really simple and terse language. This combined with strange Unicode characters for primitive functions and operators, gives it a reputation of unreadability. However, there is only a small number of functions to learn, and you get used really quickly to read them and understand what they do. Some combinations also occur so frequently that you can recognize them instantly (APL programmers call them idioms).
@@ -726,7 +780,13 @@ then \(\varphi(n)\) is true for every natural n
-
The Ising model is a model used to represent magnetic dipole moments in statistical physics. Physical details are on the Wikipedia page, but what is interesting is that it follows a complex probability distribution on a lattice, where each site can take the value +1 or -1.
The Ising model is a model used to represent magnetic dipole moments in statistical physics. Physical details are on the Wikipedia page, but what is interesting is that it follows a complex probability distribution on a lattice, where each site can take the value +1 or -1.
Mathematical definition
We have a lattice \(\Lambda\) consisting of sites \(k\). For each site, there is a moment \(\sigma_k \in \{ -1, +1 \}\). \(\sigma =
@@ -846,7 +906,23 @@ J\sigma_i \sum_{j\sim i} \sigma_j. \]
-
L-systems are a formal way to make interesting visualisations. You can use them to model a wide variety of objects: space-filling curves, fractals, biological systems, tilings, etc.
L-systems are a formal way to make interesting visualisations. You can use them to model a wide variety of objects: space-filling curves, fractals, biological systems, tilings, etc.
