The Observation Theory Encyclopedia

The verdict a group receives when it has too few rows or too few queries to score.

The fraction of all rows a classifier labels correctly, the score most easily fooled, since predicting the majority class for every row scores the majority's share.

Combining rows or groups into one number.

The normalized overlap between a consumer's average read operator and the covariance of the data on the read subspace, written kappa, between zero and one.

The assignment of a bit budget across directions.

Of a covariance, having different variances in different directions.

In a flip comparison, a third code built to destroy the consumer's read subspace at the same bits.

A row that is never or almost never retrieved as anyone's nearest neighbour.

Recall at k restricted to the rows that are rarely retrieved, the observer's outliers, reported as the minimum over strata so that a mean cannot hide the tail.

The property that support cannot increase when an itemset grows, which licenses Apriori to prune every superset of an infrequent itemset without loss.

The statement that every subset of a frequent itemset is frequent, the contrapositive of anti-monotonicity.

The operation inside a language model that lets each token look at earlier ones by comparing its query to their keys and averaging their values.

The declaration of which transformations of a column keep its meaning, any injective relabelling for nominal, a strictly increasing map for ordinal, an affine map for interval, and a positive rescaling for ratio, nested in that order.

An assignment to each feature of a share of one prediction.

A check of a number or system against its record by a reader who did not produce it, bound to a sealed file.

The area under the receiver operating characteristic curve, equal to the probability that a random positive scores above a random negative, ties counted as one half.

Fitting the same model on bootstrap resamples and averaging.

A representation of a document as a vector with one coordinate per vocabulary term holding that term's count.

The mean of the per-class recalls, so that a large class cannot hide a small one.

A threshold a statistic must reach, written down before the measurement.

The simplest scorer a claim must beat under the same protocol, chance, a constant, an untrained encoder, or a single model.

How common a cause or class is before any observation, the prior that Bayes' rule multiplies by.

A set of independent vectors whose span is the whole space, so that every vector is exactly one combination of them.

The probability of a cause given an observation, equal to the probability of the observation given the cause times the base rate, divided by the overall probability of the observation.

A Bernoulli variable is one with probability p and zero otherwise, with mean p and variance p(1 minus p).

Of a map between two spaces, neither stretching nor shrinking any distance by more than a fixed factor.

The unit of a budget.

An instrument that recovers a consumer's read operator from calls to the consumer alone, without access to its gradients or its code.

The fraction of transmitted radio blocks the receiver cannot decode, abbreviated BLER.

Dividing the significance threshold by the number of tests, which holds the family-wise error rate at or below the original threshold whatever the dependence among the tests, at the price of being conservative.

Fitting a sequence of weak scorers, each on the rows the previous ones got wrong, and summing them.

An estimate of a confidence interval made by resampling the data with replacement many times and recomputing the statistic each time.

The third element of an observer.

The finding that recovery of a read operator by a probe is a cliff at the full dimension of the space rather than a slope, and that the cliff does not move with the operator's rank.

A store of recently used data kept so that it need not be fetched again.

The property of a score that a value of 0.8 means the row is positive eighty percent of the time.

The number of distinctions a model class can draw, the model-side half of the budget.

The sampling distribution of a mean of n independent values is close to normal once n is a few dozen, whatever the shape of the values, with standard error sigma over the square root of n.

A claim, made at a time, that something is safe to act on.

A test collection built so that a shortcut which passes the benchmark fails on it.

The value a rank statistic reaches on average under a random ranking.

A piece of a document, the unit a retrieval pipeline encodes and indexes.

A consumer that produces a score per row and turns it into a decision with a threshold.

The small set of allowed values a quantizer replaces each number with.

The interval over which a changing quantity stays correlated with itself.

A cold measurement is taken before the cache holds anything useful, a warm one after.

The span of a matrix's columns, which is the set of every output the matrix can produce, of dimension equal to the rank.

The fingerprint git assigns to a snapshot of a repository and its history, which identifies the content exactly and does not by itself prove when it existed.

The expected number of steps a random walk on a graph needs to go from one node to another and back.

Of a spectrum, having a few eigenvalues that carry most of the total.

The probability of A among the repetitions in which B occurred, the probability of both divided by the probability of B.

Of a rule, the support of the rule's itemset divided by the support of its antecedent.

A range that would contain the true value in a stated fraction of repeated samples, usually 95 percent.

A variable that moves with both the treatment and the outcome so that a measured difference cannot be attributed.

The four counts a two-class classifier with a threshold produces on a test set, true and false positives and negatives, from which precision, recall, the false positive rate, and accuracy are read as conditional probabilities.

The function that acts on a vector, the first element of an observer.

A formula that reduces several axes to one verdict.

A training rule that pulls pairs declared similar together and pushes other pairs apart.

A comparison arm that should not show the effect, run beside the arm that should.

An erratum or retraction, a change to a published number or claim that the record keeps beside the original, naming what was wrong and what replaced it.

The cosine of two centred columns, between minus one and one, unchanged by shifting or rescaling either.

The dot product divided by the product of the two lengths, between minus one and one, unchanged by rescaling either vector.

The case, alignment near one, in which the read subspace and the high-variance subspace coincide and the reconstruction-optimal code is also the read-preserving one.

The expectation of the product of two variables' deviations from their means, positive when they move together, the off-diagonal entry of the covariance matrix and the numerator of the correlation.

The matrix of pairwise covariances of a set of rows, whose trace is the total variance.

The fraction of decisions a certificate clears, reported beside its false-clear rate, since a certificate that clears nothing has a false-clear rate of zero and no use.

The validation rule that an encoder votes only if its held-out AUROC on a corpus it was not trained on clears a preregistered margin over a bag-of-words null.

The expected bits per outcome when outcomes drawn from p are coded as if from a model q.

The smallest item support in an itemset over the largest, with a threshold below which the itemset is discarded.

Splitting the data into folds and evaluating on each fold a model trained on the others.

The second derivative of a consumer, which the finite difference of equation 0.8 does not read and which sets the error of the linear model at a step.

A clustering that calls a point a core point when at least a minimum number of points lie within a radius, grows clusters by reachability from core points, and leaves the rest as noise.

The set of inputs whose score equals the threshold.

A classifier that scores by a sequence of axis-aligned splits, flat within each leaf, so that its sensitivity is zero almost everywhere and its importances count splits.

A sealed statement of what a study will count, drop, or treat as a failure, written before the run.

Of a node in a graph, the number of edges it has.

The local crowding of rows around a point, the coordinate the geodesic reader of a spectral embedding discards and DBSCAN and the density detector read.

The failure in which the consumer that was evaluated is not the consumer that was deployed, or time moved between the two.

A scorer that calls a row an outlier, of four families reading distance from the mean, distance to neighbours, density relative to neighbours, or cluster membership.

For a two by two matrix, ad minus bc, the number whose vanishing means the columns are dependent and no inverse exists.

A quantizer that stores each vector's length exactly and rounds its direction.

Collapsing an ordered quantity to a few labels by binning it, so that values in one cell become indistinguishable.

The rate of a favourable decision in one group divided by the rate in another.

The narrowing of the spread of pairwise distances as dimension grows, read in the book as the reader running out of resolution.

The error a code costs a reader, the trace of the read operator against the error covariance.

The sum of the coordinatewise products of two vectors.

A change over time in what a consumer reads or in the data it reads.

Halting a boosting run when a held-out score stops improving.

The number of directions a matrix really uses, the square of the sum of its eigenvalues over the sum of their squares, defined for a nonnegative spectrum that is not all zero, with no cutoff to choose.

A direction a symmetric matrix only stretches, and the factor by which it stretches it.

A vector assigned to an object, a word, a sentence, a node, a document, so that nearness in the vector space stands for a relation between the objects.

A model that maps an input to an embedding.

A scorer that averages or votes several scorers.

The expected surprise of a distribution, the bits needed per outcome under the best code, at most the log base two of the number of outcomes.

The requirement that the true-positive rate and the false-positive rate be the same across groups.

The decision to hand an item to a person rather than decide it, the single-decision form of abstention.

A rule that produces an estimate of an unknown quantity from a sample, unbiased when its expectation over samples is that quantity.

The straight-line distance between two vectors, which reads every coordinate at the scale it arrives in.

A set of outcomes of an experiment, the thing a probability is assigned to.

Choosing what to drop when a cache is full.

The average of a random variable's values weighted by their probabilities, its long-run average over repetitions, also called the mean.

The average over score bins of the absolute difference between the mean score and the fraction of positives in the bin.

The fraction of total variance retained by a set of principal components, the identity reader's criterion for a reduction.

Twice the product of precision and recall over their sum.

The fraction of the decisions a certificate cleared in which the witness said otherwise, conditional on clearing and reported beside the certificate's coverage.

The fraction of negatives a classifier labels positive, which like recall does not depend on the base rate, so that classifiers are compared across datasets by those two and not by precision.

The probability of at least one false alarm across a set of tests, at most the number of tests times the per-test threshold by the union bound.

Continuing to train an encoder on a new objective or corpus, so that its quotient changes.

An estimate of a derivative from two evaluations of the function at points a small step apart.

At matched bits, the outcome in which the code with the worse reconstruction error scores better on the consumer's task, while a code built to destroy the read subspace scores worst.

A floor is a lower bound a quantity cannot fall below and a ceiling an upper bound it cannot exceed, each proved or measured and named as such.

The set of entries a reader reads.

A score written as a short expression in the features, such as the smaller of two features plus a third, with a threshold.

Whether a stored value is still within its coherence time when it is read.

The square root of the sum of a matrix's squared entries, which also equals the square root of the sum of its squared singular values.

A bar that a build or a claim must pass before it proceeds, with the bar and the null written down first.

The normal distribution, in many dimensions the one whose density falls with the Mahalanobis distance.

The length of the shortest path along edges between two nodes of a graph.

The cost of an alternative in a decision task is the Mahalanobis distance between the encoding of the alternative and the encoding of the task's reference point under the inverse covariance.

An evaluator-relative theory of preference, value, and choice.

The vector of a function's partial derivatives, the direction of fastest increase, whose dot product with a small step is the first-order change in the function.

The procedure that turns independent vectors into an orthonormal basis for their span, dividing the first by its length and subtracting from each next vector its projections onto the basis made so far.

A set of nodes and a set of edges joining pairs of them.

The code that evaluates a model.

A short fixed-length fingerprint of a file, computed so that any change to the file changes the fingerprint.

One attention operation.

The matrix of second derivatives of a score, whose off-diagonal entries are the interactions.

A clustering that merges the closest pair of clusters at each step, under a linkage that reads the nearest pair, the farthest, or the average, so that merge heights never decrease.

A row retrieved as a nearest neighbour far more often than chance allows.

The excess of a few rows in the nearest-neighbour lists of many queries over what the Poisson ceiling allows, measured by the busiest count and the Robin Hood index, a property of the queries.

The square matrix with ones on the diagonal and zeros elsewhere, which leaves every vector unchanged.

The consumer whose read operator is the identity, for which read distortion is mean squared error.

A per-feature score of how much a classifier reads it.

Writing a value into a missing cell that the consumer will read.

Two events are independent when knowing one changes nothing about the other, so that the probability of both is the product.

The number of directions a dataset varies along locally, whatever the number of its coordinates and whatever the number of its covariance directions.

The matrix that undoes a square matrix, so that the inverse times A times x is x.

An index that partitions vectors into cells by k-means and answers a query by searching only the cells nearest to it.

Of a covariance, having the same variance in every direction.

A set of items that appear together in a transaction.

The size of the intersection of two sets over the size of their union, between zero and one, zero exactly when the sets are disjoint, which discards joint absence.

The matrix of partial derivatives of a vector-valued consumer, whose transpose times itself averages to the read operator.

The fraction of item pairs two rankings order the same way, minus the fraction they order differently.

The directions a matrix sends to zero.

A measure of how far one probability distribution is from another, zero when they are identical.

A clustering that minimizes the sum of squared errors to the cluster centres.

The stored keys and values of earlier tokens, kept so they need not be recomputed.

How far a replica trails the primary.

Erasing one bit costs at least Boltzmann's constant times the absolute temperature times the natural log of two.

A model that reads a sequence of tokens and outputs a probability for the next one, scored by perplexity.

A matrix built from a graph's edges whose eigenvectors, from the smallest eigenvalue up, are the smoothest functions on the graph.

The truncated singular value decomposition of the term-document matrix, ordinarily uncentred, which coincides with principal components on documents only after centring.

The sample mean settles toward the expectation as the sample grows, its standard error falling with the square root of n, so that halving the error takes four times the data.

Any information in the training data that could only be known after the decision, or any identifier that lets the model recognize a row it will be tested on.

The straight line predicting one column from another that minimizes the sum of squared vertical errors, with slope the covariance over the variance of the predictor, passing through the two means, and accounting for r squared of the variance.

One of six labels every headline claim carries, proved, demonstrated, replicated, predicted, exploratory, or refuted, defined in the evidence ledger of Volume 14.

The square root of the sum of a vector's squared coordinates, Pythagoras in d dimensions, which is also the square root of the vector's dot product with itself.

A claim is licensed when it is a theorem checked in Lean in appendix C, or a measurement sealed with its commit hash before the run that survived its registered null and bar, and a chapter may rest on it.

Confidence divided by the consequent's support, so that lift one is the independence baseline.

The likelihood of a model is the probability it assigns to the observed data, and maximum likelihood chooses the parameters that make it largest, which is minimizing the total surprise the model assigns, the cross-entropy with the sample standing in for the truth.

A classifier that scores by a weighted sum, logistic regression or a linear support vector machine.

A sum of scalar multiples of vectors.

Vectors none of which is a linear combination of the others, so that the only combination giving zero has every scalar zero.

A linear classifier whose score is the sigmoid of a weighted sum, strictly between zero and one, above one half exactly on one side of the hyperplane.

The best approximation of a matrix by one of rank k in total squared error keeps the first k terms of its singular value decomposition, and the error is the sum of the squared singular values dropped, the Eckart and Young theorem.

The Euclidean distance of a row from the mean after whitening, which needs a positive-definite covariance or a pseudoinverse on its support.

A curved surface of some dimension that looks flat when viewed closely.

How far a row's score sits from the threshold.

The rule that two codes are compared only at the same bit count.

A table of numbers with n rows and d columns that sends a vector to the linear combination of its columns with the vector's coordinates as the scalars.

The mean of a sample is its average and the median its middle value once sorted.

A rule for the distance between two rows or two outputs.

The rule that a verdict over several groups is the worst group's verdict, with abstention counted as a verdict, never the average.

A strictly monotone transform of a score in either direction cannot change its optimal thresholded F1, because the sweep tries thresholds both ways.

Estimating a probability or an expectation as the fraction or average over many simulated runs, a sample proportion with standard error the square root of p(1 minus p) over N.

The inflation of false positives when many hypotheses are tested and the best is reported.

A group of eigenvalues that are equal or nearly so, whose pattern names the shape a dataset lies on against a finite list of templates.

The inflation of the variance of a repeated cross-validation estimate by one plus the ratio of test to training size times the number of repeats, because the folds are not independent.

A classifier that multiplies one-dimensional likelihoods and adds their logs, so that each feature's contribution is the same whatever the others are and it cannot read an interaction.

The unit of information measured with the natural logarithm, between 1.4426 and 1.4427 bits.

A row at minimal distance from a query.

A graph on a dataset that joins each row to its k nearest rows, or to every row within a radius.

The bell-shaped distribution with mean mu and standard deviation sigma, with about 68 percent of its mass within one standard deviation, 95 within two, and 99.7 within three, and 1.96 the multiplier for exactly 95.

The directions of the data a consumer cannot distinguish, the kernel of its read operator.

The statement that the effect under study is absent, under which a test statistic's p-value is computed.

A version of the data with the structure under test removed and everything else kept, the right comparison for any measured statistic.

The set of vectors a matrix sends to zero, also called the kernel, the directions the matrix cannot see.

A consumer, its output metric, and its budget, written as the triple in equation 1.1.

The row at which a consumer is read, or the threshold at which a classifier is scored.

Of two vectors, having dot product zero.

A square matrix with orthonormal columns, whose transpose is its inverse and which preserves every length, dot product, and angle.

A basis of unit vectors orthogonal to each other.

The matrix whose entry in row i and column j is the product of a vector's i-th and j-th coordinates, of rank at most one and positive semidefinite for a vector with itself.

A row the reader cannot place.

The rule by which a consumer's mistakes are scored, the second element of an observer.

Of a comparison, made on the same rows or seeds for both arms.

A set of rewordings of one input that preserve its meaning.

The rate of change of a function of a vector when one coordinate moves and the others stay fixed.

The value below which a given fraction of the rows fall.

The bootstrap interval that takes the 2.5th and 97.5th percentiles of a statistic recomputed on a few thousand resamples.

A quantizer that chooses a scale per coordinate.

A test that computes the p-value by reassigning the labels under the null, every way or a few thousand random ways, and counting the fraction of statistics at least as extreme as the observed.

Two to the power of the average number of bits a language model needs per token of a test text.

Of a case, built so that the answer is known before the instrument reads it, such as an affine consumer whose read operator is its weight vector's outer product.

The largest neighbour count that at least one point in a dataset would reach by chance under a Poisson null, above which a count is evidence of a hub.

The distribution of a count of rare events, the limit of the binomial when n is large and p small with np held at mu, with mean and variance both mu.

The division of every claim in a report into those asserted by design and those backed by an artifact.

A symmetric matrix whose quadratic form is positive for every nonzero vector, which is the same as every eigenvalue being positive.

Of a symmetric matrix, having every quadratic form nonnegative, as the read operator and the covariance are.

Multiplying a starting vector by a symmetric matrix and rescaling, repeatedly, so that the component along the top eigenvector grows fastest and the vector turns toward it.

The fraction of predicted positives that are truly positive, and the fraction of true positives that were predicted.

Committing the hypothesis, the bar, and the analysis before the measurement is run, so that the record shows what was predicted.

Projection of the centred data onto the eigenvectors of its covariance with the largest eigenvalues, the linear orthogonal projection of rank k that minimizes reconstruction error for the identity reader.

The fraction of repetitions in which an event would occur if the experiment were repeated without end, a number between zero and one, obeying the complement rule and the addition rule.

Splitting a vector into pieces and quantizing each piece with its own codebook.

The component of a vector along a unit direction.

A deterministic rule that produces a sequence indistinguishable from chance from a starting value, the seed, so that a simulation which records its seed reruns to the last digit and one that does not cannot.

The probability of seeing a difference at least as large as the one observed if the true difference were zero.

The number x transposed A x that a symmetric matrix assigns to a vector, a sum of the entries times pairs of coordinates.

Replacing each number with one of a small set of allowed values so that it can be stored in a few bits.

The three vectors each token produces inside attention.

The rows a retrieval benchmark asks about.

The space of data with a set of transformations declared not to matter, so that two rows differing only by such a transformation are the same point.

An ensemble of decision trees, each fit on a bootstrap sample with a random subset of features at each split.

A number attached to each outcome of an experiment, described by its distribution, the values it can take with the probability of each.

The dimension of a matrix's column space, at most the number of rows and of columns.

A bound, computed from a compressed representation, that certifies which neighbour rankings the compression preserved for a consumer and which it did not.

Of a map, preserving the ordering of distances without any bound on the stretch.

An eigenvector of the read operator with a nonzero eigenvalue, a direction the consumer is sensitive to.

The error as a consumer experiences it, the trace of the read operator times the error's second-moment matrix, which is its covariance when the error is centered.

The average outer product of a consumer's sensitivity over a dataset, an average of local linearizations whose kernel is the set of directions unread at almost every row of the workload.

The directions of the data a consumer can distinguish, spanned by the eigenvectors of its read operator with nonzero eigenvalue.

The fraction of a query's true k nearest neighbours that an index returned.

The instrument that decides whether a clustering certificate is right, wrong, or vacuous, by naming the manifold from the eigenvalue multiplets or certifying that none is present.

The squared length of the difference between a row and its approximation, the identity reader's distortion.

A claimed lower bound on how often a certificate must be renewed.

The longest renewal period that keeps a certificate within its promised error, a measured property of the system and not a convention.

An instrument's declining to report a number it cannot support.

Of a claim, bar, null, or budget, written into a sealed file before the measurement.

Zero or twice a validated encoder's held-out AUROC minus one, whichever is larger, used as that encoder's authority.

A copy of a database kept on another machine.

Reordering a candidate list with a second scorer.

What is left of a vector after its projection is subtracted, orthogonal to the direction projected onto.

Removing from a column the least-squares multiple of another.

A system that answers a question by chunking documents, embedding the chunks, indexing them, retrieving the nearest to the embedded question, and handing them to a generator.

The fraction of a total count that would have to move from points above the mean to points below it to make every count equal.

The path of true positive rate against false positive rate as the threshold sweeps, whose area is the AUROC.

A rotation applied to queries and keys that encodes where each token sits in the sequence.

A family of scores for generated text against a reference.

A rule for discarding candidates during a search that is guaranteed to discard no solution.

The average squared deviation from the sample mean with n minus 1 in the denominator, because the sample mean sits closer to its own sample than the true mean does and the deviations come out a little small.

Choosing which rows to read.

The distribution of a statistic across repeated samples of the same size, whose standard deviation is the statistic's standard error.

The number a classifier produces per row before a threshold turns it into a decision.

Of a prediction, committed with its hash recorded before the measurement was run, so that anyone with the repository can verify it has not changed, and with a public push, a signed tag, or an archival deposit to fix when.

The number that fixes a run's pseudo-randomness.

The vector of partial derivatives of a consumer with respect to each coordinate of its input, at one point.

The lecture deck of ECE 514, cited by line range from the instructor's session outlines, which are not public.

One partition of an index that is searched separately, with the results merged.

For a row, the difference between its mean distance to the nearest other cluster and its mean distance to its own cluster, divided by the larger of the two.

A reversal of a comparison when groups are combined, which the book reads as an aggregation quotient.

The size of one rank-one term of the singular value decomposition, the square root of an eigenvalue of A transposed A.

Any matrix written as a sum of rank-one outer products ordered by size, with orthonormal vectors on both sides, the eigenvector idea for a matrix that is not square.

The mean cubed deviation of a column from its mean over the cube of its spread, zero for a symmetric column.

The function that exponentiates a list of numbers and divides by their sum, so that they are positive and add to one.

The table at the end of every chapter naming, for each number, the repository, file, and line range it came from.

The set of all linear combinations of a set of vectors.

The ordinary correlation between two lists of ranks.

Clustering the rows of the row-normalized spectral embedding, which reads the angle and discards the density.

A symmetric matrix written as the sum of its eigenvalues times the outer products of its orthonormal eigenvectors.

The coordinates a node receives from its values in the first few nontrivial eigenvectors of the graph Laplacian.

The list of a matrix's eigenvalues.

A partition of the rows into a part the model is fit on and a part it is scored on.

The square root of the variance, the spread of a variable in its own units.

The spread of an estimate across repeated samples.

Subtracting a column's mean and dividing by its spread, so that it has mean zero and variance one.

Splitting rows into strata, by difficulty or by group, and scoring each separately, so that the report can take the minimum over strata.

The sum over rows of the squared distance to the row's cluster centre, the validity index k-means minimizes.

Of an itemset, the fraction of transactions that contain it.

Minus the log base two of an outcome's probability, its information in bits.

A quadratic stand-in for the consumer's output metric, the read distortion, used to allocate bits when the output itself cannot be.

Running a measurement across a range of one parameter and reading the curve.

A square matrix equal to its own transpose.

Feeding a language model the correct text as context rather than its own earlier outputs.

Comparing a measured list of numbers, such as eigenvalue ratios, to a stored list for each candidate shape and picking the smallest distance between the logarithms.

A number computed from the sample that sits near a reference value under the null and far from it otherwise, whose observed value the p-value compares with its distribution under the null.

A weighting of term counts by how rare the term is across the collection, so that a term in every document carries no weight.

The value at which a score becomes a positive decision.

A piece of text, roughly a word, the unit a language model reads and writes.

The sum of a matrix's diagonal, which for a covariance is the total variance.

One row of a market-basket table, the set of items bought together.

The one-millisecond slot in which a 5G tower schedules a transmission, abbreviated TTI.

The matrix with rows and columns swapped, written with a superscript T.

Keeping the first k components of a spectrum and dropping the rest, a bet that the consumer reads the top of the spectrum.

A type I error rejects a true null, at the rate the threshold fixes.

Equally likely to fall anywhere in an interval, with mean one half and variance one twelfth on the unit interval.

A vector of length one, a pure direction.

The value of a certificate's statistic below which the certificate is uninformative, derived from the problem rather than tuned to the data.

A score for a clustering computed without labels.

The mean squared deviation of a column from its mean, the identity reader's measure of spread.

A list of d numbers, and the arrow from the origin to the point with those coordinates.

The outcome of a registered test, pass, fail, or abstain, taken as the worst group with the groups too thin to score counted.

The allocation of a bit budget across directions that gives each direction half the log of its sensitivity-weighted variance over a common water level, and nothing to directions under the water.

The asymptotic rule for how the number of eigenvalues of a continuum Laplacian below a value grows with that value, whose exponent reveals the dimension of the space.

Rescaling centred data by the inverse square root of a positive-definite covariance, or a pseudoinverse on its support, so that the covariance becomes the identity.

Drawing rows with replacement lets a row appear more than once, as the bootstrap does, and drawing without replacement lets each appear at most once.

An independent measurement of whether a certificate's claim was true.

The bound on the best F1 a score can reach at any threshold, from the Youden index, true positive rate minus false positive rate, maximized over thresholds.

True positive rate minus false positive rate at a threshold, whose maximum over thresholds is the pointwise ceiling that prunes the formula search.

A value with the mean subtracted and the result divided by the standard deviation, the number of standard deviations it sits from the mean.