Math
Mathematics: proofs, geometry, calculus, linear algebra, probability, statistics, and math explained visually.
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The Naïve Utility Calculus as a unified, quantitative framework for action understanding sciencedirect.com
Cognitive Psychology, 2021. [All Versions]. [Project]. This paper presents a formal theory of the Naïve Utility Calculus as a probabilistic generative model, which highlights the role of cost and reward tradeoffs in a Bayesian framework for action-understanding. The model…
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Analogy between concepts sciencedirect.com
Artificial Intelligence, 2019. [All Versions]. A mathematical account on analogy.
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How to Grow a Mind: Statistics, Structure, and Abstraction science.org
Science, 2011. [All Versions]. [Preprint]. This review describes recent approaches to reverse-engineering human learning and cognitive development and, in parallel, engineering more humanlike machine learning systems. Computational models that perform probabilistic inference…
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Scientific Reduction plato.stanford.edu
Plato Stanford. A computational philosophy account on Scientific Reduction, which comes with no explicit boundary with Explanation.
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Scientific Explanation plato.stanford.edu
Plato Stanford. A computational philosophy account on Scientific Explanation, a canonical application of Abduction.
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First-order Model Theory plato.stanford.edu
Plato Stanford. A computational philosophy account on First-order Model Theory, which is a branch of mathematics that deals with the relationships between descriptions in first-order languages and the structures that satisfy these descriptions.
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Causal Models plato.stanford.edu
Plato Stanford. A computational philosophy account on Causal models, which are mathematical models representing causal relationships within an individual system or population.
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Mixtures of Dirichlet Process with Applications to Bayesian Nonparametric Problems people.eecs.berkeley.edu
The Annals of Statistics, 1974. [All Versions]. The original paper on Dirichlet Process modeling for non-parametric problems.
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Mathematical discoveries from program search with large language models nature.com
Nature, 2024. [All Versions]. Large language models (LLMs) have demonstrated tremendous capabilities in solving complex tasks, from quantitative reasoning to understanding natural language. However, LLMs sometimes suffer from confabulations (or hallucinations), which can result…
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Rational arbitration between statistics and rules in human sequence processing nature.com
Nature Human Behavior, 2022. [All Versions].
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With or Without U? The Appropriate Test for a U-Shaped Relationship mpra.ub.uni-muenchen.de
Oxford Bulletin of Economics and Statistics, 2010. [All Versions]. The original method for testing U-shape relation from the data, which is distinctive from the quadratic regression test.
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Finitely Generated Groups and First-Order Logic londmathsoc.onlinelibrary.wiley.com
Journal of The London Mathematical Society-second Series, 2005. [All Versions].
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Symbolic data analysis: what is it? link.springer.com
Proceedings in Computational Statistics, 2006. [All Versions].
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Pareto optimality in multiobjective problems link.springer.com
Applied Mathematics and Optimization, 1977. [All Versions]. The original paper on the pareto optimality in multiobjective problems.
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Beneficial and harmful explanatory machine learning link.springer.com
Machine Learning, 2021. [All Versions]. Given the recent successes of Deep Learning in AI there has been increased interest in the role and need for explanations in machine learned theories. A distinct notion in this context is that of Michie’s definition of ultra-strong…
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From information scaling of natural images to regimes of statistical models jstor.org
Quarterly of Applied Mathematics, 2008. [All Versions]. [Preprint]. One fundamental property of natural image data that distinguishes vision from other sensory tasks such as speech recognition is that scale plays a profound role in image formation and interpretation…
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A Bayesian Analysis of Some Non-parametric Problems jstor.org
The Annals of Statistics, 1973. [All Versions]. [Preprint]. A classic review on non-parametric problems.
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The Indian Buffet Process: An Introduction and Review jmlr.org
Journal of Machine Learning Research, 2011. [All Versions]. The Indian buffet process is a stochastic process defining a probability distribution over equivalence classes of sparse binary matrices with a finite number of rows and an unbounded number of columns. This…
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Probabilistic Sufficient Explanations ijcai.org
IJCAI'21, 2021. [All Versions]. Understanding the behavior of learned classifiers is an important task, and various black-box explanations, logical reasoning approaches, and model-specific methods have been proposed. This paper introduces probabilistic sufficient explanations…
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VMC: A Grammar for Visualizing Statistical Model Checks ieeexplore.ieee.org
IEEE Transactions on Visualization and Computer Graphics, 2024. [All Versions]. Visualizations play a critical role in validating and improving statistical models. However, the design space of model check visualizations is not well understood, making it difficult for authors to…
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Situation Calculus en.wikipedia.org
Wikipedia. Wikipedia on Situation Calculus, a logic formalism designed for representing and reasoning about dynamical domains.
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Nonparametric Bayesian Logic dl.acm.org
UAI'05, 2005. [All Versions]. [Preprint]. The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population…
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ShapeMOD: macro operation discovery for 3D shape programs dl.acm.org
ACM Transactions on Graphics, 2021. [All Versions]. A popular way to create detailed yet easily controllable 3D shapes is via procedural modeling, i.e. generating geometry using programs. Such programs consist of a series of instructions along with their associated parameter…
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Penrose: from mathematical notation to beautiful diagrams dl.acm.org
ACM Transactions on Graphics, 2020. [All Versions]. This work introduces a system called Penrose for creating mathematical diagrams. Its basic functionality is to translate abstract statements written in familiar math-like notation into one or more possible visual…
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Synthesis of Incremental Linear Algebra Programs dl.acm.org
ACM Transactions on Database Systems, 2020. [All Versions]. This article targets the Incremental View Maintenance (IVM) of sophisticated analytics (such as statistical models, machine learning programs, and graph algorithms) expressed as linear algebra programs. This work…
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InverseCSG: automatic conversion of 3D models to CSG trees dl.acm.org
ACM Transactions on Graphics, 2018. [All Versions]. While computer-aided design is a major part of many modern manufacturing pipelines, the design files typically generated describe raw geometry. Lost in this representation is the procedure by which these designs were…
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A Mathematical Theory of Communication cs.yale.edu
The Bell System Technical Journal, 1948. [All Versions]. Shannon's original paper on Information Theory.
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Explanation and Abductive Inference cognition.princeton.edu
The Oxford Handbook of Thinking and Reasoning, 2012. [All Versions]. This chapter reviews evidence from cognitive psychology and cognitive development concerning the structure and function of explanations, with a focus on the role of explanations in learning and inference. The…
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The naïve utility calculus: Computational principles underlying commonsense psychology cell.com
Trends in Cognitive Sciences, 2016. [All Versions]. [Preprint]. This review article proposes that human social cognition is structured around a basic understanding of ourselves and others as intuitive utility maximizers: from a young age, humans implicitly assume that agents…
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Probabilistic models of cognition: Conceptual foundations cell.com
Trends in Cognitive Sciences, 2006. [All Versions]. Remarkable progress in the mathematics and computer science of probability has led to a revolution in the scope of probabilistic models. In particular, ‘sophisticated’ probabilistic methods apply to structured relational…
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A Grammar of Hypotheses for Visualization, Data, and Analysis arxiv.org
2022. [All Versions]. This work presents a grammar for expressing hypotheses in visual data analysis to formalize the previously abstract notion of "analysis tasks." Through the lens of this grammar, the authors lay the groundwork for how a user's data analysis questions can be…
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A tale of three probabilistic families: Discriminative, descriptive, and generative models ams.org
Quarterly of Applied Mathematics, 2018. [All Versions]. [Preprint]. The pattern theory of Grenander is a mathematical framework where patterns are represented by probability models on random variables of algebraic structures. In this paper, the authors review three families of…
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Confidential-PROFITT: Confidential PROof of FaIr Training of Trees openreview.net
(ICLR) Proposes fair decision tree learning algorithms along with zero-knowledge proof protocols to obtain a proof of fairness on the audited server.
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FairProof: Confidential and Certifiable Fairness for Neural Networks arxiv.org
(Arxiv) Proposes an alternative paradigm to traditional auditing using crytographic tools like Zero-Knowledge Proofs; gives a system called FairProof for verifying fairness of small neural networks.
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(Arxiv) Systematic review of algorithm auditing studies and identification of trends in their methodological approaches.
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XAudit : A Theoretical Look at Auditing with Explanations arxiv.org
(Arxiv) Formalizes the role of explanations in auditing and investigates if and how model explanations can help audits.
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Neural Network Model Extraction Attacks in Edge Devicesby Hearing Architectural Hints arxiv.org
(arxiv) Through the acquisition of memory access events from bus snooping, layer sequence identification bythe LSTM-CTC model, layer topology connection according to the memory access pattern, and layer dimension estimation under data volume constraints, it demonstrates one can…
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Auditing Local Explanations is Hard arxiv.org
(NeurIPS) Gives the (prohibitive) query complexity of auditing explanations.
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Setting the Record Straighter on Shadow Banning arxiv.org
(INFOCOM) (Code) Considers the possibility of shadow banning in Twitter (ie, the moderation black-box algorithm), and measures the probability of several hypothesis.
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Certifying and Removing Disparate Impact arxiv.org
(SIGKDD) Proposes SVM-based methods to certify absence of bias and methods to remove biases from a dataset.
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Boccara, N. (2014). Modeling complex systems. Springer-Verlag New York. worldcat.org
An overview of important mathematical models of complex systems.
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Mandelbrot, B. (2006). The fractal geometry of nature. New York: W.H. Freeman and Company. worldcat.org
Beautiful introduction to the world of fractals.
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Calculus 1 youtube.com
Full course playlist.
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To The Point Math youtube.com
Short reviews of common algebra and calculus topics.
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Precalculus - College Algebra/Trigonometry youtube.com
Full course playlist.
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Calculus 3 youtube.com
Full course playlist.
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Differential Equations youtube.com
Full course playlist.
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Calculus 2 youtube.com
Full course playlist.
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Abstract Algebra: Harvard Extension Videos youtube.com
Benedict Gross.
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StatQuest youtube.com
Introductory video explanations of statistics, probability, and machine learning.
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