Related papers: Lecture notes on descriptional complexity and rand…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
This brief note highlights some basic concepts required toward understanding the evolution of machine learning and deep learning models. The note starts with an overview of artificial intelligence and its relationship to biological neuron…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
This graduate textbook on machine learning tells a story of how patterns in data support predictions and consequential actions. Starting with the foundations of decision making, we cover representation, optimization, and generalization as…
Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…
We present an approach for summarization from multiple documents which report on events that evolve through time, taking into account the different document sources. We distinguish the evolution of an event into linear and non-linear.…
I discuss (ontologies_and_ontological_knowledge_bases / formal_methods_and_theories) duality and its category theory extensions as a step toward a solution to Knowledge-Based Systems Theory. In particular I focus on the example of the…
How can we make sense of large-scale recordings of neural activity across learning? Theories of neural network learning with their origins in statistical physics offer a potential answer: for a given task, there are often a small set of…
A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…
A short survey about combinatorics on words and algorithmic methods in a ring. Special attention is given to Shirshov's results. Adopted for undegraduate students.
The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…
The literature on machine teaching, machine education, and curriculum design for machines is in its infancy with sparse papers on the topic primarily focusing on data and model engineering factors to improve machine learning. In this paper,…
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
This short paper discusses continually updated causal abstractions as a potential direction of future research. The key idea is to revise the existing level of causal abstraction to a different level of detail that is both consistent with…
What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…
Ontologies are a popular way of representing domain knowledge, in particular, knowledge in domains related to life sciences. (Semi-)automating the process of building an ontology has attracted researchers from different communities into a…
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most…
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…