Purged cross-validation is a variant of k-fold cross-validation designed to prevent look-ahead bias in time series and other structured data, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. It is primarily used in financial machine learning to ensure the independence of training and testing samples when labels depend on future events. It provides an alternative to conventional cross-validation and walk-forward backtesting methods, which often yield overly optimistic performance estimates due to information leakage and overfitting. == Motivation == Standard cross-validation assumes that observations are independently and identically distributed (IID), which often does not hold in time series or financial datasets. If the label of a test sample overlaps in time with the features or labels in the training set, the result may be data leakage and overfitting. Purged cross-validation addresses this issue by removing overlapping observations and, optionally, adding a temporal buffer ("embargo") around the test set to further reduce the risk of leakage. The figure below illustrates standard 5 Fold Cross-Validation == Purging == Purging removes from the training set any observation whose timestamp falls within the time range of formation of a label in the test set. This can be the case for train set observations before and after the test set. Their removal ensures that the algorithm cannot learn during train time information that will be used to assess the performance of the algorithm. See the figure below for an illustration of purging. == Embargoing == Embargoing addresses a more subtle form of leakage: even if an observation does not directly overlap the test set, it may still be affected by test events due to market reaction lag or downstream dependencies. To guard against this, a percentage-based embargo is imposed after each test fold. For example, with a 5% embargo and 1000 observations, the 50 observations following each test fold are excluded from training. Unlike purging, embargoing can only occur after the test set. The figure below illustrates the application of embargo: == Applications == Purged and embargoed cross-validation has been useful in: Backtesting of trading strategies Validation of classifiers on labeled event-driven returns Any machine learning task with overlapping label horizons == Example == To illustrate the effect of purging and embargoing, consider the figures below. Both diagrams show the structure of 5-fold cross-validation over a 20-day period. In each row, blue squares indicate training samples and red squares denote test samples. Each label is defined based on the value of the next two observations, hence creating an overlap. If this overlap is left untreated, test set information leaks into the train set. The second figure applies the Purged CV procedure. Notice how purging removes overlapping observations from the training set and the embargo widens the gap between test and training data. This approach ensures that the evaluation more closely resembles a true out-of-sample test and reduces the risk of backtest overfitting. == Combinatorial Purged Cross-Validation == Walk-forward backtesting analysis, another common cross-validation technique in finance, preserves temporal order but evaluates the model on a single sequence of test sets. This leads to high variance in performance estimation, as results are contingent on a specific historical path. Combinatorial Purged Cross-Validation (CPCV) addresses this limitation by systematically constructing multiple train-test splits, purging overlapping samples, and enforcing an embargo period to prevent information leakage. The result is a distribution of out-of-sample performance estimates, enabling robust statistical inference and more realistic assessment of a model's predictive power. === Methodology === CPCV divides a time-series dataset into N sequential, non-overlapping groups. These groups preserve the temporal order of observations. Then, all combinations of k groups (where k < N) are selected as test sets, with the remaining N − k groups used for training. For each combination, the model is trained and evaluated under strict controls to prevent leakage. To eliminate potential contamination between training and test sets, CPCV introduces two additional mechanisms: Purging: Any training observations whose label horizon overlaps with the test period are excluded. This ensures that future information does not influence model training. Embargoing: After the end of each test period, a fixed number of observations (typically a small percentage) are removed from the training set. This prevents leakage due to delayed market reactions or auto-correlated features. Each data point appears in multiple test sets across different combinations. Because test groups are drawn combinatorially, this process produces multiple backtest "paths," each of which simulates a plausible market scenario. From these paths, practitioners can compute a distribution of performance statistics such as the Sharpe ratio, drawdown, or classification accuracy. === Formal definition === Let N be the number of sequential groups into which the dataset is divided, and let k be the number of groups selected as the test set for each split. Then: The number of unique train-test combinations is given by the binomial coefficient: ( N k ) {\displaystyle {\binom {N}{k}}} Each observation is used in k {\displaystyle k} test sets and contributes to φ [ N , k ] {\displaystyle \varphi [N,k]} unique backtest paths: φ [ N , k ] = k N ( N k ) {\displaystyle \varphi [N,k]={\frac {k}{N}}{\binom {N}{k}}} This yields a distribution of performance metrics rather than a single point estimate, making it possible to apply Monte Carlo-based or probabilistic techniques to assess model robustness. === Illustrative example === Consider the case where N = 6 and k = 2. The number of possible test set combinations is ( 6 2 ) = 15 {\displaystyle {\binom {6}{2}}=15} . Each of the six groups appears in five test splits. Consequently, five distinct backtest paths can be constructed, each incorporating one appearance from every group. ==== Test group assignment matrix ==== This table shows the 15 test combinations. An "x" indicates that the corresponding group is included in the test set for that split. ==== Backtest path assignment ==== Each group contributes to five different backtest paths. The number in each cell indicates the path to which the group's result is assigned for that split. === Advantages === Combinatorial Purged Cross-Validation offers several key benefits over conventional methods: It produces a distribution of performance metrics, enabling more rigorous statistical inference. The method systematically eliminates lookahead bias through purging and embargoing. By simulating multiple historical scenarios, it reduces the dependence on any single market regime or realization. It supports high-confidence comparisons between competing models or strategies. CPCV is commonly used in quantitative strategy research, especially for evaluating predictive models such as classifiers, regressors, and portfolio optimizers. It has been applied to estimate realistic Sharpe ratios, assess the risk of overfitting, and support the use of statistical tools such as the Deflated Sharpe Ratio (DSR). === Limitations === The main limitation of CPCV stems from its high computational cost. However, this cost can be managed by sampling a finite number of splits from the space of all possible combinations.
HTK Limited
HTK Limited is a software-as-a-service company that provides mobile phone messaging and IVR services. Founded in 1996, HTK is headquartered in Ipswich, Suffolk, UK. HTK provide mass notification services. Specifically, the "Police Direct" messaging service to Suffolk and Norfolk Constabularies. In 2010 the HTK Horizon SaaS platform was selected by the Scottish Environment Protection Agency (SEPA) for their Floodline Warnings Direct service. == History == HTK was founded in 1996 by Marlon Bowser and Adrian Gregory and from the outset focused on what has now become commonly known as Software-as-a-Service. in 2004, according to the Deloitte Fast 50 (UK), HTK was the 17th fastest growing company in the East of England. In 2005 The Times listed HTK 65th nationally and 4th in the East of England in the Sunday Times & Microsoft "Tech Track 100" awards. In 2009 the company was approved as a supplier to UK Government under a new framework agreement. In 2010 HTK launched version 2.2 of its Horizon platform, with a feature set that signals a shift from mass notification into the customer service automation market.
Elastic net regularization
In statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the L1 and L2 penalties of the lasso and ridge methods. Nevertheless, elastic net regularization is typically more accurate than both methods with regard to reconstruction. == Specification == The elastic net method overcomes the limitations of the LASSO (least absolute shrinkage and selection operator) method which uses a penalty function based on ‖ β ‖ 1 = ∑ j = 1 p | β j | . {\displaystyle \|\beta \|_{1}=\textstyle \sum _{j=1}^{p}|\beta _{j}|.} Use of this penalty function has several limitations. For example, in the "large p, small n" case (high-dimensional data with few examples), the LASSO selects at most n variables before it saturates. Also if there is a group of highly correlated variables, then the LASSO tends to select one variable from a group and ignore the others. To overcome these limitations, the elastic net adds a quadratic part ( ‖ β ‖ 2 {\displaystyle \|\beta \|^{2}} ) to the penalty, which when used alone is ridge regression (known also as Tikhonov regularization). The estimates from the elastic net method are defined by β ^ ≡ argmin β ( ‖ y − X β ‖ 2 + λ 2 ‖ β ‖ 2 + λ 1 ‖ β ‖ 1 ) . {\displaystyle {\hat {\beta }}\equiv {\underset {\beta }{\operatorname {argmin} }}(\|y-X\beta \|^{2}+\lambda _{2}\|\beta \|^{2}+\lambda _{1}\|\beta \|_{1}).} The quadratic penalty term makes the loss function strongly convex, and it therefore has a unique minimum. The elastic net method includes the LASSO and ridge regression: in other words, each of them is a special case where λ 1 = λ , λ 2 = 0 {\displaystyle \lambda _{1}=\lambda ,\lambda _{2}=0} or λ 1 = 0 , λ 2 = λ {\displaystyle \lambda _{1}=0,\lambda _{2}=\lambda } . Meanwhile, the naive version of elastic net method finds an estimator in a two-stage procedure : first for each fixed λ 2 {\displaystyle \lambda _{2}} it finds the ridge regression coefficients, and then does a LASSO type shrinkage. This kind of estimation incurs a double amount of shrinkage, which leads to increased bias and poor predictions. To improve the prediction performance, sometimes the coefficients of the naive version of elastic net is rescaled by multiplying the estimated coefficients by ( 1 + λ 2 ) {\displaystyle (1+\lambda _{2})} . Examples of where the elastic net method has been applied are: Support vector machine Metric learning Portfolio optimization Cancer prognosis == Reduction to support vector machine == It was proven in 2014 that the elastic net can be reduced to the linear support vector machine. A similar reduction was previously proven for the LASSO in 2014. The authors showed that for every instance of the elastic net, an artificial binary classification problem can be constructed such that the hyper-plane solution of a linear support vector machine (SVM) is identical to the solution β {\displaystyle \beta } (after re-scaling). The reduction immediately enables the use of highly optimized SVM solvers for elastic net problems. It also enables the use of GPU acceleration, which is often already used for large-scale SVM solvers. The reduction is a simple transformation of the original data and regularization constants X ∈ R n × p , y ∈ R n , λ 1 ≥ 0 , λ 2 ≥ 0 {\displaystyle X\in {\mathbb {R} }^{n\times p},y\in {\mathbb {R} }^{n},\lambda _{1}\geq 0,\lambda _{2}\geq 0} into new artificial data instances and a regularization constant that specify a binary classification problem and the SVM regularization constant X 2 ∈ R 2 p × n , y 2 ∈ { − 1 , 1 } 2 p , C ≥ 0. {\displaystyle X_{2}\in {\mathbb {R} }^{2p\times n},y_{2}\in \{-1,1\}^{2p},C\geq 0.} Here, y 2 {\displaystyle y_{2}} consists of binary labels − 1 , 1 {\displaystyle {-1,1}} . When 2 p > n {\displaystyle 2p>n} it is typically faster to solve the linear SVM in the primal, whereas otherwise the dual formulation is faster. Some authors have referred to the transformation as Support Vector Elastic Net (SVEN), and provided the following MATLAB pseudo-code: == Software == "Glmnet: Lasso and elastic-net regularized generalized linear models" is a software which is implemented as an R source package and as a MATLAB toolbox. This includes fast algorithms for estimation of generalized linear models with ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two penalties (the elastic net) using cyclical coordinate descent, computed along a regularization path. JMP Pro 11 includes elastic net regularization, using the Generalized Regression personality with Fit Model. "pensim: Simulation of high-dimensional data and parallelized repeated penalized regression" implements an alternate, parallelised "2D" tuning method of the ℓ parameters, a method claimed to result in improved prediction accuracy. scikit-learn includes linear regression and logistic regression with elastic net regularization. SVEN, a Matlab implementation of Support Vector Elastic Net. This solver reduces the Elastic Net problem to an instance of SVM binary classification and uses a Matlab SVM solver to find the solution. Because SVM is easily parallelizable, the code can be faster than Glmnet on modern hardware. SpaSM, a Matlab implementation of sparse regression, classification and principal component analysis, including elastic net regularized regression. Apache Spark provides support for Elastic Net Regression in its MLlib machine learning library. The method is available as a parameter of the more general LinearRegression class. SAS (software) The SAS procedure Glmselect and SAS Viya procedure Regselect support the use of elastic net regularization for model selection.
Cellular evolutionary algorithm
A cellular evolutionary algorithm (cEA) is a kind of evolutionary algorithm (EA) in which individuals cannot mate arbitrarily, but every one interacts with its closer neighbors on which a basic EA is applied (selection, variation, replacement). The cellular model simulates natural evolution from the point of view of the individual, which encodes a tentative optimization, learning, or search problem solution. The essential idea of this model is to provide the EA population with a special structure defined as a connected graph, in which each vertex is an individual who communicates with his nearest neighbors. Particularly, individuals are conceptually set in a toroidal mesh, and are only allowed to recombine with close individuals. This leads to a kind of locality known as "isolation by distance". The set of potential mates of an individual is called its "neighborhood". It is known that, in this kind of algorithm, similar individuals tend to cluster creating niches, and these groups operate as if they were separate sub-populations (islands). There is no clear borderline between adjacent groups, and close niches could be easily colonized by competitive niches and potentially merge solution contents during the process. Simultaneously, farther niches can be affected more slowly. == Introduction == A cellular evolutionary algorithm (cEA) usually evolves a structured bidimensional grid of individuals, although other topologies are also possible. In this grid, clusters of similar individuals are naturally created during evolution, promoting exploration in their boundaries, while exploitation is mainly performed by direct competition and merging inside them. The grid is usually 2D toroidal structure, although the number of dimensions can be easily extended (to 3D) or reduced (to 1D, e.g. a ring). The neighborhood of a particular point of the grid (where an individual is placed) is defined in terms of the Manhattan distance from it to others in the population. Each point of the grid has a neighborhood that overlaps the neighborhoods of nearby individuals. In the basic algorithm, all the neighborhoods have the same size and identical shapes. The two most commonly used neighborhoods are L5, also called the Von Neumann or NEWS (North, East, West and South) neighborhood, and C9, also known as the Moore neighborhood. Here, L stands for "linear" while C stands for "compact". In cEAs, the individuals can only interact with their neighbors in the reproductive cycle where the variation operators are applied. This reproductive cycle is executed inside the neighborhood of each individual and, generally, consists in selecting two parents among its neighbors according to a certain criterion, applying the variation operators to them (recombination and mutation for example), and replacing the considered individual by the recently created offspring following a given criterion, for instance, replace if the offspring represents a better solution than the considered individual. == Synchronous versus asynchronous == In a regular synchronous cEA, the algorithm proceeds from the very first top left individual to the right and then to the several rows by using the information in the population to create a new temporary population. After finishing with the bottom-right last individual the temporary population is full with the newly computed individuals, and the replacement step starts. In it, the old population is completely and synchronously replaced with the newly computed one according to some criterion. Usually, the replacement keeps the best individual in the same position of both populations, that is, elitism is used. According to the update policy of the population used, an asynchronous cEA may also be defined and is a well-known issue in cellular automata. In asynchronous cEAs the order in which the individuals in the grid are update changes depending on the choice of criterion: line sweep, fixed random sweep, new random sweep, and uniform choice. All four proceed using the newly computed individual (or the original if better) for the computations of its neighbors. The overlap of the neighborhoods provides an implicit mechanism of solution migration to the cEA. Since the best solutions spread smoothly through the whole population, genetic diversity in the population is preserved longer than in non structured EAs. This soft dispersion of the best solutions through the population is one of the main issues of the good tradeoff between exploration and exploitation that cEAs perform during the search. This tradeoff can be tuned (and by extension the genetic diversity level along the evolution) by modifying (for instance) the size of the neighborhood used, as the overlap degree between the neighborhoods grows according to the size of the neighborhood. A cEA can be seen as a cellular automaton (CA) with probabilistic rewritable rules, where the alphabet of the CA is equivalent to the potential number of solutions of the problem. Hence, knowledge from research in CAs can be applied to cEAs. == Parallelism == Cellular EAs are very amenable to parallelism, thus usually found in the literature of parallel metaheuristics. In particular, fine grain parallelism can be used to assign independent threads of execution to every individual, thus allowing the whole cEA to run on a concurrent or actually parallel hardware platform. In this way, large time reductions can be obtained when running cEAs on FPGAs or GPUs. However, it is important to stress that cEAs are a model of search, in many senses different from traditional EAs. Also, they can be run in sequential and parallel platforms, reinforcing the fact that the model and the implementation are two different concepts. See here for a complete description on the fundamentals for the understanding, design, and application of cEAs.
Linguamatics
Linguamatics, headquartered in Cambridge, England, with offices in the United States and UK, is a provider of text mining systems through software licensing and services, primarily for pharmaceutical and healthcare applications. Founded in 2001, the company was purchased by IQVIA in January 2019. == Technology == The company develops enterprise search tools for the life sciences sector. The core natural language processing engine (I2E) uses a federated architecture to incorporate data from 3rd party resources. Initially developed to be used interactively through a graphic user interface, the core software also has an application programming interface that can be used to automate searches. LabKey, Penn Medicine, Atrius Health and Mercy all use Linguamatics software to extract electronic health record data into data warehouses. Linguamatics software is used by 17 of the top 20 global pharmaceutical companies, the US Food and Drug Administration, as well as healthcare providers. == Software community == The core software, "I2E", is used by a number of companies to either extend their own software or to publish their data. Copyright Clearance Center uses I2E to produce searchable indexes of material that would otherwise be unsearchable due to copyright. Thomson Reuters produces Cortellis Informatics Clinical Text Analytics, which depends on I2E to make clinical data accessible and searchable. Pipeline Pilot can integrate I2E as part of a workflow. ChemAxon can be used alongside I2E to allow named entity recognition of chemicals within unstructured data. Data sources include MEDLINE, ClinicalTrials.gov, FDA Drug Labels, PubMed Central, and Patent Abstracts.
Parkerian Hexad
The Parkerian Hexad is a set of six elements of information security proposed by Donn B. Parker in 1998. The Parkerian Hexad adds three additional attributes to the three classic security attributes of the CIA triad (confidentiality, integrity, availability). The Parkerian Hexad attributes are the following: Confidentiality Possession or Control Integrity Authenticity Availability Utility These attributes of information are atomic in that they are not broken down into further constituents; they are non-overlapping in that they refer to unique aspects of information. Any information security breach can be described as affecting one or more of these fundamental attributes of information. == Attributes from the CIA triad == === Confidentiality === Confidentiality refers to the "quality or state of being private or secret; known only to a limited few", or "the property that information is not made available or disclosed to unauthorized individuals, entities, or processes". For example: If an enterprise's strategic plans are leaked to competitors then this is a breach of confidentiality; If unauthorized persons gain access to an individual's financial records then that individual's confidentiality is breached. === Integrity === Integrity refers to being correct or consistent with the intended state of information. Any unauthorized modification of data, whether deliberate or accidental, is a breach of data integrity. For example: Data stored on disk are expected to be stable. If the data is changed at random by problems with a disk controller then this is a breach of integrity; Data generated by a medical device is transmitted and stored in the healthcare center but neither altered nor tampered with; Application programs are supposed to record information correctly. If the application introduces deviations from the intended values then this is a breach of integrity. "From Donn Parker: My definition of information integrity comes from the dictionaries. Integrity means that the information is whole, sound, and unimpaired (not necessarily correct). It means nothing is missing from the information it is complete and in intended good order". === Availability === Availability means having timely access to information. For example: A disk crash or denial-of-service attacks both cause a breach of availability. Any delay in response of a system that exceeds the expected service levels for that system can be described as a breach of availability. GPS jamming can lead to loss of Availability of the GPS system. == Parker's added attributes == === Authenticity === Authenticity is the "quality of being authentic or of established authority for truth and correctness". Parker defines it thus: "is the information genuine and accurate? Does it conform to reality and have validity?" and "authoritative, valid, true, real, genuine, or worthy of acceptance or belief by reason of conformity to fact and reality". === Possession or control === Possession or control refers to the loss of data by the authorized user (even if the ʺthiefʺ cannot access the data). From a control systems perspective, it is any loss of control (the ability to change settings and functions) or loss of view (the ability to monitor the system’s operation and its response to controls). Suppose a thief were to steal a sealed envelope containing a bank debit card and its personal identification number. Even if the thief did not open that envelope, it's reasonable for the victim to be concerned that the thief could do so at any time. That situation illustrates a loss of control or possession of information but does not involve the breach of confidentiality. === Utility === Utility refers to the data's usefulness. For example: Suppose someone encrypted data on disk to prevent unauthorized access or undetected modifications–and then lost the decryption key: that would be a breach of utility. The data would be confidential, controlled, integral, authentic, and available–they just wouldn't be useful in that form. The conversion of salary data from one currency into an inappropriate currency would be a breach of utility, as would the storage of data in a format inappropriate for a specific computer architecture; e.g., EBCDIC instead of ASCII or 9-track magnetic tape instead of DVD-ROM. A tabular representation of data substituted for a graph could be described as a breach of utility if the substitution made it more difficult to interpret the data. Utility is often confused with availability because breaches such as those described in these examples may also require time to work around the change in data format or presentation. However, the concept of usefulness is distinct from that of availability.
Distributional Soft Actor Critic
Distributional Soft Actor Critic (DSAC) is a suite of model-free off-policy reinforcement learning algorithms, tailored for learning decision-making or control policies in complex systems with continuous action spaces. Distinct from traditional methods that focus solely on expected returns, DSAC algorithms are designed to learn a Gaussian distribution over stochastic returns, called value distribution. This focus on Gaussian value distribution learning notably diminishes value overestimations, which in turn boosts policy performance. Additionally, the value distribution learned by DSAC can also be used for risk-aware policy learning. From a technical standpoint, DSAC is essentially a distributional adaptation of the well-established soft actor-critic (SAC) method. To date, the DSAC family comprises two iterations: the original DSAC-v1 and its successor, DSAC-T (also known as DSAC-v2), with the latter demonstrating superior capabilities over the Soft Actor-Critic (SAC) in Mujoco benchmark tasks. The source code for DSAC-T can be found at the following URL: Jingliang-Duan/DSAC-T. Both iterations have been integrated into an advanced, Pytorch-powered reinforcement learning toolkit named GOPS: GOPS (General Optimal control Problem Solver).