# probabilistic Published articles for probabilistic. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Bloom Filters vs Counting Bloom Filters: When Deletions Kill Performance DevFeed: [Bloom Filters vs Counting Bloom Filters: When Deletions Kill Performance]() Original publisher: [Read original article]() Author: hello@ankit-rana.com Published: 2026-03-17T00:00:00Z Content type: article Language: en Sources: [Ankit Rana | Mechanical Sympathy]() Topics: [Algorithms](), [Caching](), [CPU Cache]() Tags: [bloom-filter](), [cache](), [cpu](), [cpu-cache](), [data-structures](), [distributed-systems](), [false-negative](), [false-positives](), [memory](), [performance](), [probabilistic](), [systems]() ### AI overview The article explains that standard Bloom filters support membership checks but not deletion because clearing shared bits can create false negatives. Counting Bloom filters enable deletion with counters, but their larger memory footprint can push lookups out of CPU cache and increase latency through random memory access. ### Source excerpt A standard Bloom filter is append-only because bits are shared between items, so clearing a bit for one item can create a false negative for another. Counting Bloom filters fix deletion by replacing each bit with a 4-bit or 8-bit counter, which multiplies the footprint four to eight times, pushes the structure out of L3, and turns each of the k lookups into a roughly 100 ns RAM hit instead of a 10 ns cache hit. ## Cuckoo Filters: Cache-Friendly Membership Checks With Deletions DevFeed: [Cuckoo Filters: Cache-Friendly Membership Checks With Deletions]() Original publisher: [Read original article]() Author: hello@ankit-rana.com Published: 2026-03-17T00:00:00Z Content type: tutorial Language: en Sources: [Ankit Rana | Mechanical Sympathy]() Topics: [CPU Cache](), [Caching](), [hash]() Tags: [cache](), [capacity](), [cpu-cache](), [cuckoo-filter](), [data-structures](), [false-positive](), [hash](), [insert](), [performance](), [probabilistic](), [spatial-locality](), [systems]() ### AI overview This article explains how Cuckoo filters support deletions while improving CPU cache behavior compared with counting Bloom filters. They check two specific buckets using compact fingerprints, but insertions can fail when kick-out chains exceed their limit, requiring capacity planning or overflow handling. ### Source excerpt A Cuckoo filter stores a one-to-two byte fingerprint in a hash table and finds it by checking exactly two buckets, the primary index and its XOR-derived alternate, instead of k random bit positions scattered across a large array. That spatial locality is the whole win on real CPUs. The trade-off is a hard edge: when the kick-out chain exceeds its limit, the insert fails outright. ## SlowerLogLog DevFeed: [SlowerLogLog]() Original publisher: [Read original article]() Author: Evan Miller Published: 2020-02-06T18:00:00Z Content type: article Language: en Sources: [Evan Miller]() Topics: [Data structures](), [Algorithm](), [math](), [hash](), [implementation]() Tags: [algorithm](), [data-structure](), [hash](), [implementation](), [math](), [probabilistic]() ### AI overview This article introduces SlowerLogLog, a variation of HyperLogLog for estimating the number of unique elements in a set. It explains how Maximum Likelihood Estimation can estimate cardinality and standard error, support small cardinalities, and avoid requiring a power-of-two register count. The method is easier to derive and implement but much more computationally expensive because each element is hashed once per register. ### Source excerpt What rolls down stairs and counts unique items imprecisely? HyperLogLog. Also SlowerLogLog ## Deep Probabilistic Modelling with Gaussian Processes #NIPS2017 DevFeed: [Deep Probabilistic Modelling with Gaussian Processes #NIPS2017]() Original publisher: [Read original article]() Published: 2017-12-04T12:00:00Z Content type: tutorial Language: en Sources: [Alex Korbonits]() Topics: [Tutorial](), [VAE](), [Machine learning](), [Deep learning](), [Neural Network](), [NeurIPS]() Tags: [analysis](), [bias](), [conference](), [data](), [deep-learning](), [gaussian](), [inference](), [modelling](), [neural-network](), [neurips](), [probabilistic](), [research](), [supervised-learning](), [theory](), [tutorial](), [unsupervised-learning](), [videos]() ### AI overview Lecture notes from a NeurIPS 2017 tutorial introduce deep probabilistic modelling with Gaussian processes, covering probabilistic neural networks, uncertainty, graphical models, and the computational challenge of inference. ### Source excerpt Lecture notes from Neil Lawrence's NIPS 2017 tutorial on deep probabilistic modelling with Gaussian processes -- from GPs to deep GPs and variational inference. ## Simulating a Biased Coin with a Fair Coin DevFeed: [Simulating a Biased Coin with a Fair Coin]() Original publisher: [Read original article]() Published: 2014-02-12T10:00:51Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Computer science](), [Algorithm](), [Algorithms, Complexity](), [Python](), [Mathematics]() Tags: [algorithm](), [calculus](), [coins](), [computational-complexity](), [convergent-series](), [floating-point](), [mathematics](), [probabilistic](), [programming](), [python]() ### AI overview This guest article presents a Python algorithm for simulating a biased coin using a fair coin. It reads the intended probability's binary expansion and compares each bit with an independent fair random bit, returning when they differ. The method produces probability exactly equal to the intended bias, including for irrational probabilities, and has constant expected running time when the probability's bits are efficiently computable. ### Source excerpt This is a guest post by my friend and colleague Adam Lelkes. Adam's interests are in algebra and theoretical computer science. This gem came up because Adam gave a talk on probabilistic computation in which he discussed this technique. Problem: simulate a biased coin using a fair coin. Solution: (in Python) def biasedCoin(binaryDigitStream, fairCoin): for d in binaryDigitStream: if fairCoin() != d: return d Discussion: This function takes two arguments, an iterator representing the binary expansion of the intended probability of getting 1 (let us denote it as $ p$) and another function that returns 1 or 0 with equal probability. ## Simulating a Fair Coin with a Biased Coin DevFeed: [Simulating a Fair Coin with a Biased Coin]() Original publisher: [Read original article]() Published: 2014-02-08T19:03:46Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Computer science](), [Mathematics](), [Python]() Tags: [algebra](), [coins](), [guest-post](), [mathematics](), [probabilistic](), [python](), [random-number-generators](), [science]() ### AI overview This tutorial explains von Neumann's method for simulating a fair coin using a biased coin. It examines pairs of independent flips, discards matching pairs, returns the first result when the pair differs, and derives the expected number of flips. ### Source excerpt This is a guest post by my friend and colleague Adam Lelkes. Adam's interests are in algebra and theoretical computer science. This gem came up because Adam gave a talk on probabilistic computation in which he discussed this technique. Problem: Simulate a fair coin given only access to a biased coin. Solution: (in Python) def fairCoin(biasedCoin): coin1, coin2 = 0,0 while coin1 == coin2: coin1, coin2 = biasedCoin(), biasedCoin() return coin1 Discussion: This is originally von Neumann's clever idea. ## Miller-Rabin Primality Test DevFeed: [Miller-Rabin Primality Test]() Original publisher: [Read original article]() Published: 2013-06-16T18:55:40Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Python](), [Algorithms](), [Algorithms, Complexity](), [Cryptography]() Tags: [algorithm](), [algorithms](), [complexity-theory](), [computational-complexity](), [cryptography](), [miller-rabin](), [primes](), [probabilistic](), [programming](), [python](), [random-number-generators](), [randomized-algorithm](), [rsa]() ### AI overview This tutorial explains the Miller-Rabin primality test, including its probabilistic error bound, Python implementation, and role in testing whether numbers are prime. It also discusses the algorithm's relevance to cryptography and complexity theory. ### Source excerpt Problem: Determine if a number is prime, with an acceptably small error rate. Solution: (in Python) import random def decompose(n): exponentOfTwo = 0 while n % 2 == 0: n = n/2 exponentOfTwo += 1 return exponentOfTwo, n def isWitness(possibleWitness, p, exponent, remainder): possibleWitness = pow(possibleWitness, remainder, p) if possibleWitness == 1 or possibleWitness == p - 1: return False for _ in range(exponent): possibleWitness = pow(possibleWitness, 2, p) if possibleWitness == p - 1: return False return True def probablyPrime(p, accuracy=100): if p == 2 or p == 3: return True if p < 2: return False exponent, remainder = decompose(p - 1) for _ in range(accuracy): possibleWitness = random. ## Probabilistic Bounds -- A Primer DevFeed: [Probabilistic Bounds -- A Primer]() Original publisher: [Read original article]() Published: 2013-04-15T11:14:32Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Algorithms, Complexity](), [math](), [Learning](), [Streaming]() Tags: [algorithm](), [algorithms](), [chebyshev](), [chernoff](), [chernoff-bound](), [inequality](), [learning-theory](), [machine-learning](), [markov](), [mathematics](), [probabilistic](), [probabilistic-method](), [probability-theory](), [random-variables](), [streaming](), [streaming-algorithms](), [variance]() ### AI overview This tutorial introduces probabilistic bounds used in algorithm analysis, machine learning theory, randomized algorithms, and streaming algorithms. It focuses on the Chernoff bound and presents simpler bounds from Markov's and Chebyshev's inequalities, including short proofs. ### Source excerpt Probabilistic arguments are a key tool for the analysis of algorithms in machine learning theory and probability theory. They also assume a prominent role in the analysis of randomized and streaming algorithms, where one imposes a restriction on the amount of storage space an algorithm is allowed to use for its computations (usually sublinear in the size of the input). While a whole host of probabilistic arguments are used, one theorem in particular (or family of theorems) is ubiquitous: the Chernoff bound. ## Probability Theory -- A Primer DevFeed: [Probability Theory -- A Primer]() Original publisher: [Read original article]() Published: 2013-01-04T13:45:54Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [math](), [Statistics](), [Machine Learning & Artificial Intelligence]() Tags: [expectation](), [mathematics](), [primer](), [probabilistic](), [probability-theory](), [random-variables](), [set-theory](), [statistics](), [theory](), [variables](), [variance]() ### AI overview A primer on finite probability theory that introduces probability spaces, random variables, terminology, and basic results using naive set theory. It emphasizes mathematical formalism rather than real-world applications. ### Source excerpt It is a wonder that we have yet to officially write about probability theory on this blog. Probability theory underlies a huge portion of artificial intelligence, machine learning, and statistics, and a number of our future posts will rely on the ideas and terminology we lay out in this post. Our first formal theory of machine learning will be deeply ingrained in probability theory, we will derive and analyze probabilistic learning algorithms, and our entire treatment of mathematical finance will be framed in terms of random variables. ## On Chomsky and the Two Cultures of Statistical Learning DevFeed: [On Chomsky and the Two Cultures of Statistical Learning]() Original publisher: [Read original article]() Published: 2011-05-27T00:00:00Z Content type: article Language: en Sources: [Peter Norvig]() Topics: [Statistics](), [Language models](), [Machine learning](), [syntax]() Tags: [essay](), [history-of-science](), [language-models](), [probabilistic](), [science](), [statistics]() ### AI overview This essay responds to Steven Pinker and Noam Chomsky on the role and success of statistical and probabilistic models in language. It argues that interpreting success as approximating unanalyzed data is not novel, and uses examples from language modeling, communication, gravitation, and statistical mechanics to distinguish trained, probabilistic, continuous, and quantitative models. ### Source excerpt At the MIT 150 symposium, Chomsky said that the notion of success used by statistical language models (namely, that they successfully predict the world and allow programs to accomplish tasks) was "very novel ... I don't know of anything like it in the history of science." This essay argues that it is not novel at all, but perfectly commonplace.