# conditional probability Published articles for conditional probability. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## The Philosophy of Machine Learning, or: What Comes After Hegel? DevFeed: [The Philosophy of Machine Learning, or: What Comes After Hegel?]() Original publisher: [Read original article]() Published: 2026-04-09T00:00:00Z Content type: opinion Language: en Sources: [Alex Korbonits]() Topics: [Automated reasoning](), [Artificial Intelligence](), [LLMs](), [Math and Logic](), [pattern matching]() Tags: [ai](), [automated-reasoning](), [conditional-probability](), [llms](), [logic](), [machine-learning](), [pattern-matching](), [reasoning]() ### AI overview This opinion essay compares large language models with Kant's distinction between a priori structures and a posteriori experience. It argues that LLMs learn patterns from human text but lack reliable logical scaffolding, and presents automated reasoning systems such as SMT solvers and theorem provers as a possible complement. ### Source excerpt A notebook entry that maps AI paradigms onto the history of Western philosophy -- from scholasticism to Hegel -- and asks what comes next when the current moment exhausts itself. ## One definition of algorithmic fairness: statistical parity DevFeed: [One definition of algorithmic fairness: statistical parity]() Original publisher: [Read original article]() Published: 2015-10-19T09:00:00Z Content type: opinion Language: en Sources: [Jeremy Kun]() Topics: [Algorithms](), [Algorithms, Complexity]() Tags: [algorithm](), [algorithms](), [bias](), [conditional-probability](), [discrimination](), [fairness](), [machine-learning](), [mathematics](), [programming](), [python](), [research](), [reverse-tokenism](), [self-fulfilling-prophecy](), [statistics]() ### AI overview The article examines statistical parity as one mathematical definition of algorithmic fairness. It explains the protected-group and population model, defines bias as the difference in positive classification rates between the complement and the protected group, and discusses the definition's intuitive basis and limitations. ### Source excerpt If you haven't read the first post on fairness, I suggest you go back and read it because it motivates why we're talking about fairness for algorithms in the first place. In this post I'll describe one of the existing mathematical definitions of "fairness," its origin, and discuss its strengths and shortcomings. Before jumping in I should remark that nobody has found a definition which is widely agreed as a good definition of fairness in the same way we have for, say, the security of a random number generator. ## The Boosting Margin, or Why Boosting Doesn't Overfit DevFeed: [The Boosting Margin, or Why Boosting Doesn't Overfit]() Original publisher: [Read original article]() Published: 2015-09-21T11:33:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [machine learning overfitting](), [Machine learning](), [generalization in machine learning](), [Occam's razor machine learning](), [Algorithm]() Tags: [algorithm](), [boosting](), [chernoff-bound](), [classficiation](), [complexity](), [conditional-probability](), [error](), [machine-learning](), [margins](), [mathematics](), [model](), [occam-s-razor](), [overfitting](), [training-data](), [vc-dimension]() ### AI overview This article explains why boosting can continue improving generalization after reaching zero training error. It introduces the margin-based theoretical explanation for this behavior and defines the confidence and margin of AdaBoost classifiers. ### Source excerpt There's a well-understood phenomenon in machine learning called overfitting. The idea is best shown by a graph: overfitting Let me explain. The vertical axis represents the error of a hypothesis. The horizontal axis represents the complexity of the hypothesis. The blue curve represents the error of a machine learning algorithm's output on its training data, and the red curve represents the generalization of that hypothesis to the real world. The overfitting phenomenon is marker in the middle of the graph, before which the training error and generalization error both go down, but after which the training error continues to fall while the generalization error rises. ## Martingales and the Optional Stopping Theorem DevFeed: [Martingales and the Optional Stopping Theorem]() Original publisher: [Read original article]() Published: 2014-03-03T10:00:38Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [math]() Tags: [2-sat](), [conditional-probability](), [expectation](), [gambling](), [martingales](), [mathematics](), [optional-stopping-theorem](), [primer](), [probability-theory](), [random](), [random-variables](), [randomized-algorithm](), [stochastic-processes](), [theory]() ### AI overview This primer introduces martingales as models of fair betting games and explains their connection to probability theory. It begins with a geometric-distribution exercise involving repeated die throws, then introduces the ABRACADABRA problem using a monkey typing random letters. ### Source excerpt This is a guest post by my colleague Adam Lelkes. The goal of this primer is to introduce an important and beautiful tool from probability theory, a model of fair betting games called martingales. In this post I will assume that the reader is familiar with the basics of probability theory. For those that need to refresh their knowledge, Jeremy's excellent primers (1, 2) are a good place to start. ## Linear Regression DevFeed: [Linear Regression]() Original publisher: [Read original article]() Published: 2013-08-18T17:43:20Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [linear-regression](), [Machine learning](), [data]() Tags: [conditional-probability](), [covariance](), [data](), [expectation](), [linear-regression](), [machine-learning](), [python](), [regression](), [statistics](), [variance]() ### AI overview This tutorial introduces linear regression as a basic form of statistical learning. It explains independent and dependent variables, uses a two-variable linear model to predict one variable from another, and describes estimating the model parameters from sample pairs. ### Source excerpt Machine learning is broadly split into two camps, statistical learning and non-statistical learning. The latter we've started to get a good picture of on this blog; we approached Perceptrons, decision trees, and neural networks from a non-statistical perspective. And generally "statistical" learning is just that, a perspective. Data is phrased in terms of independent and dependent variables, and statistical techniques are leveraged against the data. In this post we'll focus on the simplest example of this, linear regression, and in the sequel see it applied to various learning problems. ## Conditional (Partitioned) Probability -- A Primer DevFeed: [Conditional (Partitioned) Probability -- A Primer]() Original publisher: [Read original article]() Published: 2013-03-28T13:36:09Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [math](), [function]() Tags: [bayes-theorem](), [conditional-probability](), [mathematics](), [partitions](), [primer](), [probability-theory](), [random-variables](), [set](), [theory]() ### AI overview A mathematically rigorous primer on conditional probability. It reviews finite probability spaces, probability mass functions, events, random variables, and partitions as tools for decomposing events and variables and reasoning about total probability. ### Source excerpt One of the main areas of difficulty in elementary probability, and one that requires the highest levels of scrutiny and rigor, is conditional probability. The ideas are simple enough: that we assign probabilities relative to the occurrence of some event. But shrewd applications of conditional probability (and in particular, efficient ways to compute conditional probability) are key to successful applications of this subject. This is the basis for Nate Silver's success, the logical flaws of many a political pundit, and the ability for a robot to tell where it is in an environment.