Mirella Lapata is a computer scientist and Professor in the School of Informatics at the University of Edinburgh. Working on the general problem of extracting semantic information from large bodies of text, Lapata develops computer algorithms and models in the field of natural language processing (NLP). == Education == Lapata obtained a Master of Arts (MA) degree from Carnegie Mellon University and subsequently earned a doctorate from the University of Edinburgh. Lapata's doctoral research investigated the acquisition of information from polysemous linguistic units using probabilistic methods supervised by Alex Lascarides, Chris Brew and Steve Finch. == Career and research == After her doctorate, Lapata assumed academic positions at Saarland University and at the Department of Computer Science at the University of Sheffield. At the University of Edinburgh she became a reader in the School of Informatics where she is a full Professor and holds a personal chair in natural language processing. Lapata is a member of the Human Communication Research Center and Institute for Language, Cognition and Computation, both in Edinburgh. Between 2015 and 2017, Lapata served as a member of the Royal Society Machine Learning Working Group. Recently Lapata was granted a European Research Council (ERC) Consolidator Grant worth €1.9M to fund five years of her project, TransModal: Translating from Multiple Modalities into Text. === Awards and honours === In 2009 Lapata became the first recipient of the Microsoft British Computer Society (BCS)/BCS IRSG Karen Spärck Jones Award. The award recognises achievement in furthering the progress in information retrieval and natural language processing; the award commemorates the life and work of Karen Spärck Jones. In 2012 Lapata won an Empirical Methods in Natural Language Processing (EMNLP)-CoNLL 2012 Best Reviewer Award. In 2018 Lapata was awarded, alongside Li Dong, an Association for Computational Linguistics (ACL) Best Paper Honorable Mention. In 2019 Lapata was elected a Fellow of the Royal Society of Edinburgh In 2020 Lapata was elected to the Academia Europaea. In 2025 Lapata was awarded the BCS Lovelace Medal for Computing Research.
Zeuthen strategy
The Zeuthen strategy in cognitive science is a negotiation strategy used by some artificial agents. Its purpose is to measure the willingness to risk conflict. An agent will be more willing to risk conflict if it does not have much to lose in case that the negotiation fails. In contrast, an agent is less willing to risk conflict when it has more to lose. The value of a deal is expressed in its utility. An agent has much to lose when the difference between the utility of its current proposal and the conflict deal is high. When both agents use the monotonic concession protocol, the Zeuthen strategy leads them to agree upon a deal in the negotiation set. This set consists of all conflict free deals, which are individually rational and Pareto optimal, and the conflict deal, which maximizes the Nash product. The strategy was introduced in 1930 by the Danish economist Frederik Zeuthen. == Three key questions == The Zeuthen strategy answers three open questions that arise when using the monotonic concession protocol, namely: Which deal should be proposed at first? On any given round, who should concede? In case of a concession, how much should the agent concede? The answer to the first question is that any agent should start with its most preferred deal, because that deal has the highest utility for that agent. The second answer is that the agent with the smallest value of Risk(i,t) concedes, because the agent with the lowest utility for the conflict deal profits most from avoiding conflict. To the third question, the Zeuthen strategy suggests that the conceding agent should concede just enough raise its value of Risk(i,t) just above that of the other agent. This prevents the conceding agent to have to concede again in the next round. == Risk == Risk ( i , t ) = { 1 U i ( δ ( i , t ) ) = 0 U i ( δ ( i , t ) ) − U i ( δ ( j , t ) ) U i ( δ ( i , t ) ) otherwise {\displaystyle {\text{Risk}}(i,t)={\begin{cases}1&U_{i}(\delta (i,t))=0\\{\frac {U_{i}(\delta (i,t))-U_{i}(\delta (j,t))}{U_{i}(\delta (i,t))}}&{\text{otherwise}}\end{cases}}} Risk(i,t) is a measurement of agent i's willingness to risk conflict. The risk function formalizes the notion that an agent's willingness to risk conflict is the ratio of the utility that agent would lose by accepting the other agent's proposal to the utility that agent would lose by causing a conflict. Agent i is said to be using a rational negotiation strategy if at any step t + 1 that agent i sticks to his last proposal, Risk(i,t) > Risk(j,t). == Sufficient concession == If agent i makes a sufficient concession in the next step, then, assuming that agent j is using a rational negotiation strategy, if agent j does not concede in the next step, he must do so in the step after that. The set of all sufficient concessions of agent i at step t is denoted SC(i, t). == Minimal sufficient concession == δ ′ = arg max δ ∈ S C ( A , t ) { U A ( δ ) } {\displaystyle \delta '=\arg \max _{\delta \in {SC(A,t)}}\{U_{A}(\delta )\}} is the minimal sufficient concession of agent A in step t. Agent A begins the negotiation by proposing δ ( A , 0 ) = arg max δ ∈ N S U A ( δ ) {\displaystyle \delta (A,0)=\arg \max _{\delta \in {NS}}U_{A}(\delta )} and will make the minimal sufficient concession in step t + 1 if and only if Risk(A,t) ≤ Risk(B,t). Theorem If both agents are using Zeuthen strategies, then they will agree on δ = arg max δ ′ ∈ N S { π ( δ ′ ) } , {\displaystyle \delta =\arg \max _{\delta '\in {NS}}\{\pi (\delta ')\},} that is, the deal which maximizes the Nash product. Proof Let δA = δ(A,t). Let δB = δ(B,t). According to the Zeuthen strategy, agent A will concede at step t {\displaystyle t} if and only if R i s k ( A , t ) ≤ R i s k ( B , t ) . {\displaystyle Risk(A,t)\leq Risk(B,t).} That is, if and only if U A ( δ A ) − U A ( δ B ) U A ( δ A ) ≤ U B ( δ B ) − U B ( δ A ) U B ( δ B ) {\displaystyle {\frac {U_{A}(\delta _{A})-U_{A}(\delta _{B})}{U_{A}(\delta _{A})}}\leq {\frac {U_{B}(\delta _{B})-U_{B}(\delta _{A})}{U_{B}(\delta _{B})}}} U B ( δ B ) ( U A ( δ A ) − U A ( δ B ) ) ≤ U A ( δ A ) ( U B ( δ B ) − U B ( δ A ) ) {\displaystyle U_{B}(\delta _{B})(U_{A}(\delta _{A})-U_{A}(\delta _{B}))\leq U_{A}(\delta _{A})(U_{B}(\delta _{B})-U_{B}(\delta _{A}))} U A ( δ A ) U B ( δ B ) − U A ( δ B ) U B ( δ B ) ≤ U A ( δ A ) U B ( δ B ) − U A ( δ A ) U B ( δ A ) {\displaystyle U_{A}(\delta _{A})U_{B}(\delta _{B})-U_{A}(\delta _{B})U_{B}(\delta _{B})\leq U_{A}(\delta _{A})U_{B}(\delta _{B})-U_{A}(\delta _{A})U_{B}(\delta _{A})} − U A ( δ B ) U B ( δ B ) ≤ − U A ( δ A ) U B ( δ A ) {\displaystyle -U_{A}(\delta _{B})U_{B}(\delta _{B})\leq -U_{A}(\delta _{A})U_{B}(\delta _{A})} U A ( δ A ) U B ( δ A ) ≤ U A ( δ B ) U B ( δ B ) {\displaystyle U_{A}(\delta _{A})U_{B}(\delta _{A})\leq U_{A}(\delta _{B})U_{B}(\delta _{B})} π ( δ A ) ≤ π ( δ B ) {\displaystyle \pi (\delta _{A})\leq \pi (\delta _{B})} Thus, Agent A will concede if and only if δ A {\displaystyle \delta _{A}} does not yield the larger product of utilities. Therefore, the Zeuthen strategy guarantees a final agreement that maximizes the Nash Product.
Natarajan dimension
In the theory of Probably Approximately Correct Machine Learning, the Natarajan dimension characterizes the complexity of learning a set of functions, generalizing from the Vapnik–Chervonenkis dimension for boolean functions to multi-class functions. Originally introduced as the Generalized Dimension by Natarajan, it was subsequently renamed the Natarajan Dimension by Haussler and Long. == Definition == Let H {\displaystyle H} be a set of functions from a set X {\displaystyle X} to a set Y {\displaystyle Y} . H {\displaystyle H} shatters a set C ⊂ X {\displaystyle C\subset X} if there exist two functions f 0 , f 1 ∈ H {\displaystyle f_{0},f_{1}\in H} such that For every x ∈ C , f 0 ( x ) ≠ f 1 ( x ) {\displaystyle x\in C,f_{0}(x)\neq f_{1}(x)} . For every B ⊂ C {\displaystyle B\subset C} , there exists a function h ∈ H {\displaystyle h\in H} such that for all x ∈ B , h ( x ) = f 0 ( x ) {\displaystyle x\in B,h(x)=f_{0}(x)} and for all x ∈ C − B , h ( x ) = f 1 ( x ) {\displaystyle x\in C-B,h(x)=f_{1}(x)} . The Natarajan dimension of H is the maximal cardinality of a set shattered by H {\displaystyle H} . It is easy to see that if | Y | = 2 {\displaystyle |Y|=2} , the Natarajan dimension collapses to the Vapnik–Chervonenkis dimension. Shalev-Shwartz and Ben-David present comprehensive material on multi-class learning and the Natarajan dimension, including uniform convergence and learnability. Recently, Cohen et al showed that the Natarajan dimension is the dominant term governing agnostic multi-class PAC learnability.
CN2 algorithm
The CN2 induction algorithm is a learning algorithm for rule induction. It is designed to work even when the training data is imperfect. It is based on ideas from the AQ algorithm and the ID3 algorithm. As a consequence it creates a rule set like that created by AQ but is able to handle noisy data like ID3. == Description of algorithm == The algorithm must be given a set of examples, TrainingSet, which have already been classified in order to generate a list of classification rules. A set of conditions, SimpleConditionSet, which can be applied, alone or in combination, to any set of examples is predefined to be used for the classification. routine CN2(TrainingSet) let the ClassificationRuleList be empty repeat let the BestConditionExpression be Find_BestConditionExpression(TrainingSet) if the BestConditionExpression is not nil then let the TrainingSubset be the examples covered by the BestConditionExpression remove from the TrainingSet the examples in the TrainingSubset let the MostCommonClass be the most common class of examples in the TrainingSubset append to the ClassificationRuleList the rule 'if ' the BestConditionExpression ' then the class is ' the MostCommonClass until the TrainingSet is empty or the BestConditionExpression is nil return the ClassificationRuleList routine Find_BestConditionExpression(TrainingSet) let the ConditionalExpressionSet be empty let the BestConditionExpression be nil repeat let the TrialConditionalExpressionSet be the set of conditional expressions, {x and y where x belongs to the ConditionalExpressionSet and y belongs to the SimpleConditionSet}. remove all formulae in the TrialConditionalExpressionSet that are either in the ConditionalExpressionSet (i.e., the unspecialized ones) or null (e.g., big = y and big = n) for every expression, F, in the TrialConditionalExpressionSet if F is statistically significant and F is better than the BestConditionExpression by user-defined criteria when tested on the TrainingSet then replace the current value of the BestConditionExpression by F while the number of expressions in the TrialConditionalExpressionSet > user-defined maximum remove the worst expression from the TrialConditionalExpressionSet let the ConditionalExpressionSet be the TrialConditionalExpressionSet until the ConditionalExpressionSet is empty return the BestConditionExpression
Sample exclusion dimension
In computational learning theory, sample exclusion dimensions arise in the study of exact concept learning with queries. In algorithmic learning theory, a concept over a domain X is a Boolean function over X. Here we only consider finite domains. A partial approximation S of a concept c is a Boolean function over Y ⊆ X {\displaystyle Y\subseteq X} such that c is an extension to S. Let C be a class of concepts and c be a concept (not necessarily in C). Then a specifying set for c w.r.t. C, denoted by S is a partial approximation S of c such that C contains at most one extension to S. If we have observed a specifying set for some concept w.r.t. C, then we have enough information to verify a concept in C with at most one more mind change. The exclusion dimension, denoted by XD(C), of a concept class is the maximum of the size of the minimum specifying set of c' with respect to C, where c' is a concept not in C.
Software construction
Software construction is the process of creating working software via coding and integration. The process includes unit and integration testing although does not include higher level testing such as system testing. Construction is an aspect of the software development lifecycle and is integrated in the various software development process models with varying focus on construction as an activity separate from other activities. In the waterfall model, a software development effort consists of sequential phases including requirements analysis, design, and planning which are prerequisites for starting construction. In an iterative model such as scrum, evolutionary prototyping, or extreme programming, construction as an activity that occurs concurrently or overlapping other activities. Construction planning may include defining the order in which components are created and integrated, the software quality management processes, and the allocation of tasks to teams and developers. To facilitate project management, numerous construction aspects can be measured; these include the amount of code developed, modified, reused, and destroyed, code complexity, code inspection statistics, faults-fixed and faults-found rates, and effort expended. These measurements can be useful for aspects such as ensuring quality and improving the process. == Activities == Construction includes many activities. === Coding === The following are a few of the key aspects of the coding activity: Naming Choice of name for each identifier. One study showed that the effort required to debug a program is minimized when variable names are between 10 and 16 characters. Logic Organization into statements and routines Highly cohesive routines proved to be less error prone than routines with lower cohesion. A study of 450 routines found that 50 percent of the highly cohesive routines were fault free compared to only 18 percent of routines with low cohesion. Another study of a different 450 routines found that routines with the highest coupling-to-cohesion ratios had 7 times as many errors as those with the lowest coupling-to-cohesion ratios and were 20 times as costly to fix. Although studies showed inconclusive results regarding the correlation between routine sizes and the rate of errors in them, but one study found that routines with fewer than 143 lines of code were 2.4 times less expensive to fix than larger routines. Another study showed that the code needed to be changed least when routines averaged 100 to 150 lines of code. Another study found that structural complexity and amount of data in a routine were correlated with errors regardless of its size. Interfaces between routines are some of the most error-prone areas of a program. One study showed that 39 percent of all errors were errors in communication between routines. Unused parameters are correlated with an increased error rate. In one study, only 17 to 29 percent of routines with more than one unreferenced variable had no errors, compared to 46 percent in routines with no unused variables. The number of parameters of a routine should be 7 at maximum as research has found that people generally cannot keep track of more than about seven chunks of information at once. One experiment showed that designs which access arrays sequentially, rather than randomly, result in fewer variables and fewer variable references. One experiment found that loops-with-exit are more comprehensible than other kinds of loops. Regarding the level of nesting in loops and conditionals, studies have shown that programmers have difficulty comprehending more than three levels of nesting. Control flow complexity has been shown to correlate with low reliability and frequent errors. Modularity Structuring and refactoring the code into classes, packages and other structures. When considering containment, the maximum number of data members in a class shouldn't exceed 7±2. Research has shown that this number is the number of discrete items a person can remember while performing other tasks. When considering inheritance, the number of levels in the inheritance tree should be limited. Deep inheritance trees have been found to be significantly associated with increased fault rates. When considering the number of routines in a class, it should be kept as small as possible. A study on C++ programs has found an association between the number of routines and the number of faults. A study by NASA showed that the putting the code into well-factored classes can double the code reusability compared to the code developed using functional design. Error handling Encoding logic to handle both planned and unplanned errors and exceptions. Resource management Managing computational resource use via exclusion mechanisms and discipline in accessing serially reusable resources, including threads or database locks. Security Prevention of code-level security breaches such as buffer overrun and array index overflow. Optimization Optimization while avoiding premature optimization. Documentation Both embedded in the code as comments and as external documents. === Integration === Integration is about combining separately constructed parts. Concerns include planning the sequence in which components will be integrated, creating scaffolding to support interim versions of the software, determining the degree of testing and quality work performed on components before they are integrated, and determining points in the project at which interim versions are tested. === Testing === Testing can reduce the time between when faulty logic is inserted in the code and when it is detected. In some cases, testing is performed after code has been written, but in test-first programming, test cases are created before code is written. Construction includes at least two forms of testing, often performed by the developer who wrote the code: unit testing and integration testing. === Reuse === Software reuse entails more than creating and using libraries. It requires formalizing the practice of reuse by integrating reuse processes and activities into the software life cycle. The tasks related to reuse in software construction during coding and testing may include: selection of the reusable code, evaluation of code or test re-usability, reporting reuse metrics. === Quality assurance === Techniques for ensuring quality as software is constructed include: Testing One study found that the average defect detection rates of Unit testing and integration testing are 30% and 35% respectively. Software inspection With respect to software inspection, one study found that the average defect detection rate of formal code inspections is 60%. Regarding the cost of finding defects, a study found that code reading detected 80% more faults per hour than testing. Another study shown that it costs six times more to detect design defects by using testing than by using inspections. A study by IBM showed that only 3.5 hours were needed to find a defect through code inspections versus 15–25 hours through testing. Microsoft has found that it takes 3 hours to find and fix a defect by using code inspections and 12 hours to find and fix a defect by using testing. In a 700 thousand lines program, it was reported that code reviews were several times as cost-effective as testing. Studies found that inspections result in 20% - 30% fewer defects per 1000 lines of code than less formal review practices and that they increase productivity by about 20%. Formal inspections will usually take 10% - 15% of the project budget and will reduce overall project cost. Researchers found that having more than 2 - 3 reviewers on a formal inspection doesn't increase the number of defects found, although the results seem to vary depending on the kind of material being inspected. Technical review With respect to technical review, one study found that the average defect detection rates of informal code reviews and desk checking are 25% and 40% respectively. Walkthroughs were found to have a defect detection rate of 20% - 40%, but were found also to be expensive especially when project pressures increase. Code reading was found by NASA to detect 3.3 defects per hour of effort versus 1.8 defects per hour for testing. It also finds 20% - 60% more errors over the life of the project than different kinds of testing. A study of 13 reviews about review meetings, found that 90% of the defects were found in preparation for the review meeting while only around 10% were found during the meeting. Static analysis With respect to Static analysis (IEEE1028), studies have shown that a combination of these techniques needs to be used to achieve a high defect detection rate. Other studies showed that different people tend to find different defects. One study found that the extreme programming practices of pair programming, desk checking, unit testing, integration testing, and regression testing can achieve a 90% defect detection rate. An experiment involving exper
Probit model
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit. The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model. A probit model is a popular specification for a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is most often estimated using the maximum likelihood procedure, such an estimation being called a probit regression. == Conceptual framework == Suppose a response variable Y is binary, that is it can have only two possible outcomes which we will denote as 1 and 0. For example, Y may represent presence/absence of a certain condition, success/failure of some device, answer yes/no on a survey, etc. We also have a vector of regressors X, which are assumed to influence the outcome Y. Specifically, we assume that the model takes the form P ( Y = 1 ∣ X ) = Φ ( X T β ) , {\displaystyle P(Y=1\mid X)=\Phi (X^{\operatorname {T} }\beta ),} where P is the probability and Φ {\displaystyle \Phi } is the cumulative distribution function (CDF) of the standard normal distribution. The parameters β are typically estimated by maximum likelihood. It is possible to motivate the probit model as a latent variable model. Suppose there exists an auxiliary random variable Y ∗ = X T β + ε , {\displaystyle Y^{\ast }=X^{T}\beta +\varepsilon ,} where ε ~ N(0, 1). Then Y can be viewed as an indicator for whether this latent variable is positive: Y = { 1 Y ∗ > 0 0 otherwise } = { 1 X T β + ε > 0 0 otherwise } {\displaystyle Y=\left.{\begin{cases}1&Y^{}>0\\0&{\text{otherwise}}\end{cases}}\right\}=\left.{\begin{cases}1&X^{\operatorname {T} }\beta +\varepsilon >0\\0&{\text{otherwise}}\end{cases}}\right\}} The use of the standard normal distribution causes no loss of generality compared with the use of a normal distribution with an arbitrary mean and standard deviation, because adding a fixed amount to the mean can be compensated by subtracting the same amount from the intercept, and multiplying the standard deviation by a fixed amount can be compensated by multiplying the weights by the same amount. To see that the two models are equivalent, note that P ( Y = 1 ∣ X ) = P ( Y ∗ > 0 ) = P ( X T β + ε > 0 ) = P ( ε > − X T β ) = P ( ε < X T β ) by symmetry of the normal distribution = Φ ( X T β ) {\displaystyle {\begin{aligned}P(Y=1\mid X)&=P(Y^{\ast }>0)\\&=P(X^{\operatorname {T} }\beta +\varepsilon >0)\\&=P(\varepsilon >-X^{\operatorname {T} }\beta )\\&=P(\varepsilon