Planner (often seen in publications as "PLANNER" although it is not an acronym) is a programming language designed by Carl Hewitt at MIT, and first published in 1969. First, subsets such as Micro-Planner and Pico-Planner were implemented, and then essentially the whole language was implemented as Popler by Julian Davies at the University of Edinburgh in the POP-2 programming language. Derivations such as QA4, Conniver, QLISP and Ether (see scientific community metaphor) were important tools in artificial intelligence research in the 1970s, which influenced commercial developments such as Knowledge Engineering Environment (KEE) and Automated Reasoning Tool (ART). == Procedural approach versus logical approach == The two major paradigms for constructing semantic software systems were procedural and logical. The procedural paradigm was epitomized by Lisp which featured recursive procedures that operated on list structures. The logical paradigm was epitomized by uniform proof procedure resolution-based derivation (proof) finders. According to the logical paradigm it was “cheating” to incorporate procedural knowledge. == Procedural embedding of knowledge == Planner was invented for the purposes of the procedural embedding of knowledge and was a rejection of the resolution uniform proof procedure paradigm, which Converted everything to clausal form. Converting all information to clausal form is problematic because it hides the underlying structure of the information. Then used resolution to attempt to obtain a proof by contradiction by adding the clausal form of the negation of the theorem to be proved. Using only resolution as the rule of inference is problematical because it hides the underlying structure of proofs. Also, using proof by contradiction is problematical because the axiomatizations of all practical domains of knowledge are inconsistent in practice. Planner was a kind of hybrid between the procedural and logical paradigms because it combined programmability with logical reasoning. Planner featured a procedural interpretation of logical sentences where an implication of the form (P implies Q) can be procedurally interpreted in the following ways using pattern-directed invocation: Forward chaining (antecedently): If assert P, assert Q If assert not Q, assert not P Backward chaining (consequently) If goal Q, goal P If goal not P, goal not Q In this respect, the development of Planner was influenced by natural deductive logical systems (especially the one by Frederic Fitch [1952]). == Micro-planner implementation == A subset called Micro-Planner was implemented by Gerry Sussman, Eugene Charniak and Terry Winograd and was used in Winograd's natural-language understanding program SHRDLU, Eugene Charniak's story understanding work, Thorne McCarty's work on legal reasoning, and some other projects. This generated a great deal of excitement in the field of AI. It also generated controversy because it proposed an alternative to the logic approach that had been one of the mainstay paradigms for AI. At SRI International, Jeff Rulifson, Jan Derksen, and Richard Waldinger developed QA4 which built on the constructs in Planner and introduced a context mechanism to provide modularity for expressions in the database. Earl Sacerdoti and Rene Reboh developed QLISP, an extension of QA4 embedded in INTERLISP, providing Planner-like reasoning embedded in a procedural language and developed in its rich programming environment. QLISP was used by Richard Waldinger and Karl Levitt for program verification, by Earl Sacerdoti for planning and execution monitoring, by Jean-Claude Latombe for computer-aided design, by Nachum Dershowitz for program synthesis, by Richard Fikes for deductive retrieval, and by Steven Coles for an early expert system that guided use of an econometric model. Computers were expensive. They had only a single slow processor and their memories were very small by comparison with today. So Planner adopted some efficiency expedients including the following: Backtracking was adopted to economize on the use of time and storage by working on and storing only one possibility at a time in exploring alternatives. A unique name assumption was adopted to save space and time by assuming that different names referred to different objects. For example, names like Peking (previous PRC capital name) and Beijing (current PRC capital transliteration) were assumed to refer to different objects. A closed-world assumption could be implemented by conditionally testing whether an attempt to prove a goal exhaustively failed. Later this capability was given the misleading name "negation as failure" because for a goal G it was possible to say: "if attempting to achieve G exhaustively fails then assert (Not G)." == The genesis of Prolog == Gerry Sussman, Eugene Charniak, Seymour Papert and Terry Winograd visited the University of Edinburgh in 1971, spreading the news about Micro-Planner and SHRDLU and casting doubt on the resolution uniform proof procedure approach that had been the mainstay of the Edinburgh Logicists. At the University of Edinburgh, Bruce Anderson implemented a subset of Micro-Planner called PICO-PLANNER, and Julian Davies (1973) implemented essentially all of Planner. According to Donald MacKenzie, Pat Hayes recalled the impact of a visit from Papert to Edinburgh, which had become the "heart of artificial intelligence's Logicland," according to Papert's MIT colleague, Carl Hewitt. Papert eloquently voiced his critique of the resolution approach dominant at Edinburgh "…and at least one person upped sticks and left because of Papert." The above developments generated tension among the Logicists at Edinburgh. These tensions were exacerbated when the UK Science Research Council commissioned Sir James Lighthill to write a report on the AI research situation in the UK. The resulting report [Lighthill 1973; McCarthy 1973] was highly critical although SHRDLU was favorably mentioned. Pat Hayes visited Stanford where he learned about Planner. When he returned to Edinburgh, he tried to influence his friend Bob Kowalski to take Planner into account in their joint work on automated theorem proving. "Resolution theorem-proving was demoted from a hot topic to a relic of the misguided past. Bob Kowalski doggedly stuck to his faith in the potential of resolution theorem proving. He carefully studied Planner.”. Kowalski [1988] states "I can recall trying to convince Hewitt that Planner was similar to SL-resolution." But Planner was invented for the purposes of the procedural embedding of knowledge and was a rejection of the resolution uniform proof procedure paradigm. Colmerauer and Roussel recalled their reaction to learning about Planner in the following way: "While attending an IJCAI convention in September ‘71 with Jean Trudel, we met Robert Kowalski again and heard a lecture by Terry Winograd on natural language processing. The fact that he did not use a unified formalism left us puzzled. It was at this time that we learned of the existence of Carl Hewitt’s programming language, Planner. The lack of formalization of this language, our ignorance of Lisp and, above all, the fact that we were absolutely devoted to logic meant that this work had little influence on our later research." In the fall of 1972, Philippe Roussel implemented a language called Prolog (an abbreviation for PROgrammation en LOGique – French for "programming in logic"). Prolog programs are generically of the following form (which is a special case of the backward-chaining in Planner): When goal Q, goal P1 and ... and goal Pn Prolog duplicated the following aspects of Micro-Planner: Pattern directed invocation of procedures from goals (i.e. backward chaining) An indexed data base of pattern-directed procedures and ground sentences. Giving up on the completeness paradigm that had characterized previous work on theorem proving and replacing it with the programming language procedural embedding of knowledge paradigm. Prolog also duplicated the following capabilities of Micro-Planner which were pragmatically useful for the computers of the era because they saved space and time: Backtracking control structure Unique Name Assumption by which different names are assumed to refer to distinct entities, e.g., Peking and Beijing are assumed to be different. Reification of Failure. The way that Planner established that something was provable was to successfully attempt it as a goal and the way that it establish that something was unprovable was to attempt it as a goal and explicitly fail. Of course the other possibility is that the attempt to prove the goal runs forever and never returns any value. Planner also had a (not expression) construct which succeeded if expression failed, which gave rise to the “Negation as Failure” terminology in Planner. Use of the Unique Name Assumption and Negation as Failure became more questionable when attention turned to Open Systems. The following capabiliti
Equalized odds
Equalized odds, also referred to as conditional procedure accuracy equality and disparate mistreatment, is a measure of fairness in machine learning. A classifier satisfies this definition if the subjects in the protected and unprotected groups have equal true positive rate and equal false positive rate, satisfying the formula: P ( R = + | Y = y , A = a ) = P ( R = + | Y = y , A = b ) y ∈ { + , − } ∀ a , b ∈ A {\displaystyle P(R=+|Y=y,A=a)=P(R=+|Y=y,A=b)\quad y\in \{+,-\}\quad \forall a,b\in A} For example, A {\displaystyle A} could be gender, race, or any other characteristics that we want to be free of bias, while Y {\displaystyle Y} would be whether the person is qualified for the degree, and the output R {\displaystyle R} would be the school's decision whether to offer the person to study for the degree. In this context, higher university enrollment rates of African Americans compared to whites with similar test scores might be necessary to fulfill the condition of equalized odds, if the "base rate" of Y {\displaystyle Y} differs between the groups. The concept was originally defined for binary-valued Y {\displaystyle Y} . In 2017, Woodworth et al. generalized the concept further for multiple classes.
Dendrogram
A dendrogram is a diagram representing a tree graph. This diagrammatic representation is frequently used in different contexts: in hierarchical clustering, it illustrates the arrangement of the clusters produced by the corresponding analyses. in computational biology, it shows the clustering of genes or samples, sometimes in the margins of heatmaps. in phylogenetics, it displays the evolutionary relationships among various biological taxa. In this case, the dendrogram is also called a phylogenetic tree. The name dendrogram derives from the two ancient greek words δένδρον (déndron), meaning "tree", and γράμμα (grámma), meaning "drawing, mathematical figure". == Clustering example == For a clustering example, suppose that five taxa ( a {\displaystyle a} to e {\displaystyle e} ) have been clustered by UPGMA based on a matrix of genetic distances. The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to which the data belong, with the arrows representing the distance (dissimilarity). The distance between merged clusters is monotone, increasing with the level of the merger: the height of each node in the plot is proportional to the value of the intergroup dissimilarity between its two daughters (the nodes on the right representing individual observations all plotted at zero height).
Feature selection
In machine learning, feature selection is the process of selecting a subset of relevant features (variables, predictors) for use in model construction. Feature selection techniques are used for several reasons: simplification of models to make them easier to interpret, shorter training times, to avoid the curse of dimensionality, improve the compatibility of the data with a certain learning model class, to encode inherent symmetries present in the input space. The central premise when using feature selection is that data sometimes contains features that are redundant or irrelevant, and can thus be removed without incurring much loss of information. Redundancy and irrelevance are two distinct notions, since one relevant feature may be redundant in the presence of another relevant feature with which it is strongly correlated. Feature extraction creates new features from functions of the original features, whereas feature selection finds a subset of the features. Feature selection techniques are often used in domains where there are many features and comparatively few samples (data points). == Introduction == A feature selection algorithm can be seen as the combination of a search technique for proposing new feature subsets, along with an evaluation measure which scores the different feature subsets. The simplest algorithm is to test each possible subset of features finding the one which minimizes the error rate. This is an exhaustive search of the space, and is computationally intractable for all but the smallest of feature sets. The choice of evaluation metric heavily influences the algorithm, and it is these evaluation metrics which distinguish between the three main categories of feature selection algorithms: wrappers, filters and embedded methods. Wrapper methods use a predictive model to score feature subsets. Each new subset is used to train a model, which is tested on a hold-out set. Counting the number of mistakes made on that hold-out set (the error rate of the model) gives the score for that subset. As wrapper methods train a new model for each subset, they are very computationally intensive, but usually provide the best performing feature set for that particular type of model or typical problem. Filter methods use a proxy measure instead of the error rate to score a feature subset. This measure is chosen to be fast to compute, while still capturing the usefulness of the feature set. Common measures include the mutual information, the pointwise mutual information, Pearson product-moment correlation coefficient, Relief-based algorithms, and inter/intra class distance or the scores of significance tests for each class/feature combinations. Filters are usually less computationally intensive than wrappers, but they produce a feature set which is not tuned to a specific type of predictive model. This lack of tuning means a feature set from a filter is more general than the set from a wrapper, usually giving lower prediction performance than a wrapper. However the feature set doesn't contain the assumptions of a prediction model, and so is more useful for exposing the relationships between the features. Many filters provide a feature ranking rather than an explicit best feature subset, and the cut off point in the ranking is chosen via cross-validation. Filter methods have also been used as a preprocessing step for wrapper methods, allowing a wrapper to be used on larger problems. One other popular approach is the Recursive Feature Elimination algorithm, commonly used with Support Vector Machines to repeatedly construct a model and remove features with low weights. Embedded methods are a catch-all group of techniques which perform feature selection as part of the model construction process. The exemplar of this approach is the LASSO method for constructing a linear model, which penalizes the regression coefficients with an L1 penalty, shrinking many of them to zero. Any features which have non-zero regression coefficients are 'selected' by the LASSO algorithm. Improvements to the LASSO include Bolasso which bootstraps samples; Elastic net regularization, which combines the L1 penalty of LASSO with the L2 penalty of ridge regression; and FeaLect which scores all the features based on combinatorial analysis of regression coefficients. AEFS further extends LASSO to nonlinear scenario with autoencoders. These approaches tend to be between filters and wrappers in terms of computational complexity. In traditional regression analysis, the most popular form of feature selection is stepwise regression, which is a wrapper technique. It is a greedy algorithm that adds the best feature (or deletes the worst feature) at each round. The main control issue is deciding when to stop the algorithm. In machine learning, this is typically done by cross-validation. In statistics, some criteria are optimized. This leads to the inherent problem of nesting. More robust methods have been explored, such as branch and bound and piecewise linear network. == Subset selection == Subset selection evaluates a subset of features as a group for suitability. Subset selection algorithms can be broken up into wrappers, filters, and embedded methods. Wrappers use a search algorithm to search through the space of possible features and evaluate each subset by running a model on the subset. Wrappers can be computationally expensive and have a risk of over fitting to the model. Filters are similar to wrappers in the search approach, but instead of evaluating against a model, a simpler filter is evaluated. Embedded techniques are embedded in, and specific to, a model. Many popular search approaches use greedy hill climbing, which iteratively evaluates a candidate subset of features, then modifies the subset and evaluates if the new subset is an improvement over the old. Evaluation of the subsets requires a scoring metric that grades a subset of features. Exhaustive search is generally impractical, so at some implementor (or operator) defined stopping point, the subset of features with the highest score discovered up to that point is selected as the satisfactory feature subset. The stopping criterion varies by algorithm; possible criteria include: a subset score exceeds a threshold, a program's maximum allowed run time has been surpassed, etc. Alternative search-based techniques are based on targeted projection pursuit which finds low-dimensional projections of the data that score highly: the features that have the largest projections in the lower-dimensional space are then selected. Search approaches include: Exhaustive Best first Simulated annealing Genetic algorithm Greedy forward selection Greedy backward elimination Particle swarm optimization Targeted projection pursuit Scatter search Variable neighborhood search Two popular filter metrics for classification problems are correlation and mutual information, although neither are true metrics or 'distance measures' in the mathematical sense, since they fail to obey the triangle inequality and thus do not compute any actual 'distance' – they should rather be regarded as 'scores'. These scores are computed between a candidate feature (or set of features) and the desired output category. There are, however, true metrics that are a simple function of the mutual information; see here. Other available filter metrics include: Class separability Error probability Inter-class distance Probabilistic distance Entropy Consistency-based feature selection Correlation-based feature selection == Optimality criteria == The choice of optimality criteria is difficult as there are multiple objectives in a feature selection task. Many common criteria incorporate a measure of accuracy, penalised by the number of features selected. Examples include Akaike information criterion (AIC) and Mallows's Cp, which have a penalty of 2 for each added feature. AIC is based on information theory, and is effectively derived via the maximum entropy principle. Other criteria are Bayesian information criterion (BIC), which uses a penalty of log n {\displaystyle {\sqrt {\log {n}}}} for each added feature, minimum description length (MDL) which asymptotically uses log n {\displaystyle {\sqrt {\log {n}}}} , Bonferroni / RIC which use 2 log p {\displaystyle {\sqrt {2\log {p}}}} , maximum dependency feature selection, and a variety of new criteria that are motivated by false discovery rate (FDR), which use something close to 2 log p q {\displaystyle {\sqrt {2\log {\frac {p}{q}}}}} . A maximum entropy rate criterion may also be used to select the most relevant subset of features. == Structure learning == Filter feature selection is a specific case of a more general paradigm called structure learning. Feature selection finds the relevant feature set for a specific target variable whereas structure learning finds the relationships between all the variables, usually by expressing these relationships as a graph. The most common structure learning algorithms
LogitBoost
In machine learning and computational learning theory, LogitBoost is a boosting algorithm formulated by Jerome Friedman, Trevor Hastie, and Robert Tibshirani. The original paper casts the AdaBoost algorithm into a statistical framework. Specifically, if one considers AdaBoost as a generalized additive model and then applies the cost function of logistic regression, one can derive the LogitBoost algorithm. == Minimizing the LogitBoost cost function == LogitBoost can be seen as a convex optimization. Specifically, given that we seek an additive model of the form f = ∑ t α t h t {\displaystyle f=\sum _{t}\alpha _{t}h_{t}} the LogitBoost algorithm minimizes the logistic loss: ∑ i log ( 1 + e − y i f ( x i ) ) {\displaystyle \sum _{i}\log \left(1+e^{-y_{i}f(x_{i})}\right)}
Summify
Summify was a social news aggregator founded by Mircea Paşoi and Cristian Strat, two former Google and Microsoft interns from Romania. The service emailed its users a periodic summary of news articles shared from their social networks based on their relevance and importance. The platform supported Twitter, Facebook, and Google Reader accounts. == History == In 2009, Paşoi and Strat created ReadFu, a plugin that provided a contextual summary and statistics of the target page of a hyperlink. In January 2010, ReadFu was accepted into the Vancouver-based start-up incubator Bootup Labs. On March 20, 2010 the service was renamed to Summify and a private beta began. On August 11, 2010 Paşoi and Strat announced a new direction for the service. It would become a real-time social news reader that aggregates incoming news from social networks and displays articles by importance using social reactions. After some feedback that the users preferred article digests by email more than the real-time news reader version, Summify discontinued the news reader version. In March 2011, Summify completed a Seed round, with investors including Rob Glaser, Accel Partners, and Stewart Butterfield. Summify received coverage from various news and media outlets such as TechCrunch. It was also featured in various news platforms, such as Time, The Globe and Mail, Mashable, VentureBeat, Gizmodo, Lifehacker, and The Next Web. Summify released a free app on the Apple App Store on July 8, 2011. The app allowed users to read their web summaries from iOS mobile devices. Summify was acquired by Twitter on January 19, 2012. The service shut down soon after, on June 22, 2012.
(1+ε)-approximate nearest neighbor search
(1+ε)-approximate nearest neighbor search is a variant of the nearest neighbor search problem. A solution to the (1+ε)-approximate nearest neighbor search is a point or multiple points within distance (1+ε) R from a query point, where R is the distance between the query point and its true nearest neighbor. Reasons to approximate nearest neighbor search include the space and time costs of exact solutions in high-dimensional spaces (see curse of dimensionality) and that in some domains, finding an approximate nearest neighbor is an acceptable solution. Approaches for solving (1+ε)-approximate nearest neighbor search include k-d trees, locality-sensitive hashing and brute-force search.