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.
Avizo (software)
Avizo (pronounce: 'a-VEE-zo') is a general-purpose commercial software application for scientific and industrial data visualization and analysis. Avizo is developed by Thermo Fisher Scientific and was originally designed and developed by the Visualization and Data Analysis Group at Zuse Institute Berlin (ZIB) under the name Amira. Avizo was commercially released in November 2007. For the history of its development, see the Wikipedia article about Amira. == Overview == Avizo is a software application which enables users to perform interactive visualization and computation on 3D data sets. The Avizo interface is modelled on the visual programming. Users manipulate data and module components, organized in an interactive graph representation (called Pool), or in a Tree view. Data and modules can be interactively connected together, and controlled with several parameters, creating a visual processing network whose output is displayed in a 3D viewer. With this interface, complex data can be interactively explored and analyzed by applying a controlled sequence of computation and display processes resulting in a meaningful visual representation and associated derived data. == Application areas == Avizo has been designed to support different types of applications and workflows from 2D and 3D image data processing to simulations. It is a versatile and customizable visualization tool used in many fields: Scientific visualization Materials Research Tomography, Microscopy, etc. Nondestructive testing, Industrial Inspection, and Visual Inspection Computer-aided Engineering and simulation data post-processing Porous medium analysis Civil Engineering Seismic Exploration, Reservoir Engineering, Microseismic Monitoring, Borehole Imaging Geology, Digital Rock Physics (DRP), Earth Sciences Archaeology Food technology and agricultural science Physics, Chemistry Climatology, Oceanography, Environmental Studies Astrophysics == Features == Data import: 2D and 3D image stack and volume data: from microscopes (electron, optical), X-ray tomography (CT, micro-/nano-CT, synchrotron), neutron tomography and other acquisition devices (MRI, radiography, GPR) Geometric models (such as point sets, line sets, surfaces, grids) Numerical simulation data (such as Computational fluid dynamics or Finite element analysis data) Molecular data Time series and animations Seismic data Well logs 4D Multivariate Climate Models 2D/3D data visualization: Volume rendering Digital Volume Correlation Visualization of sections, through various slicing and clipping methods Isosurface rendering Polygonal meshes Scalar fields, Vector fields, Tensor representations, Flow visualization (Illuminated Streamlines, Stream Ribbons) Image processing: 2D/3D Alignment of image slices, Image registration Image filtering Mathematical Morphology (erode, dilate, open, close, tophat) Watershed Transform, Distance Transform Image segmentation 3D models reconstruction: Polygonal surface generation from segmented objects Generation of tetrahedral grids Surface reconstruction from point clouds Skeletonization (reconstruction of dendritic, porous or fracture network) Surface model simplification Quantification and analysis: Measurements and statistics Analysis spreadsheet and charting Material properties computation, based on 3D images: Absolute permeability Thermal conductivity Molecular diffusivity Electrical resistivity/formation factor 3D image-based meshing for CFD and FEA: From 3D imaging modalities (CT, micro-CT, MRI, etc.) Surface and volume meshes generation Export to FEA and CFD solvers for simulation Post-processing for simulation analysis Presentation, automation: MovieMaker, Multiscreen, Video wall, collaboration, and VR support TCL Scripting, C++ extension API Avizo is based on Open Inventor 3D graphics toolkits (FEI Visualization Sciences Group).
Léon Bottou
Léon-Yves Bottou (French pronunciation: [leɔ̃ bɔtu]; born 1965) is a researcher best known for his work in machine learning and data compression. His work presents stochastic gradient descent as a fundamental learning algorithm. He is also one of the main creators of the DjVu image compression technology (together with Yann LeCun and Patrick Haffner), and the maintainer of DjVuLibre, the open source implementation of DjVu. He is the original developer of the Lush programming language. == Life == Léon Bottou was born in France in 1965. He obtained the Diplôme d'Ingénieur from École Polytechnique in 1987, a Magistère de Mathématiques Fondamentales et Appliquées et d’Informatique from École Normale Supérieure in 1988, a Diplôme d'Études Approndies in Computer Science in 1988, in 1988, and a PhD from Université Paris-Sud in 1991. In 1988, in collaboration with Yann LeCun, he published SN, a software package for simulating artificial neural networks. His master's thesis concerned using Time Delay Neural Networks for speech recognition. He then joined the Adaptive Systems Research Department at AT&T Bell Laboratories in Holmdel, New Jersey, where he collaborated with Vladimir Vapnik on local learning algorithms. in 1992, he returned to France and founded Neuristique S.A., a company that produced machine learning tools and one of the first data mining software packages, including Lush, an object-oriented programming language based on C and Lisp designed for training and using large-scale neural networks. In 1995, he returned to Bell Laboratories, where he developed a number of new machine learning methods, such as Graph Transformer Networks (similar to conditional random field), and applied them to handwriting recognition and OCR. The bank check recognition system that he helped develop was widely deployed by NCR and other companies, reading over 10% of all the checks in the US in the late 1990s and early 2000s. In 1996, he joined AT&T Labs and worked primarily on the DjVu image compression technology, that is used by some websites, notably the Internet Archive, to distribute scanned documents. Between 2002 and 2010, he was a research scientist at NEC Laboratories in Princeton, New Jersey, where he focused on the theory and practice of machine learning with large-scale datasets, on-line learning, and stochastic optimization methods. He developed the open source software LaSVM for fast large-scale support vector machine, and stochastic gradient descent software for training linear SVM and Conditional Random Fields. In 2010 he joined the Microsoft adCenter in Redmond, Washington, and in 2012 became a Principal Researcher at Microsoft Research in New York City. In March 2015 he joined Facebook Artificial Intelligence Research, also in New York City, as a research lead. His work in gradient descent argued that both stochastic gradient descent and batch gradient descent reach similar levels of loss with the same number of training samples, but SGD is faster when running on large datasets. He also argued that second-order gradient descent methods, such as quasi-Newton methods, can be beneficial compared to plain SGD. See (Bottou et al 2018) for a review. He was program chair of the 2013 Conference on Neural Information Processing Systems and the 2009 International Conference on Machine Learning. In 2007, he was received one of the first Blavatnik Awards for Young Scientists from the Blavatnik Family Foundation and the New York Academy of Sciences.
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Hidden layer
In artificial neural networks, a hidden layer is a layer of artificial neurons that is neither an input layer nor an output layer. The simplest examples appear in multilayer perceptrons (MLP), as illustrated in the diagram. An MLP without any hidden layer is essentially just a linear model. With hidden layers and activation functions, however, nonlinearity is introduced into the model. In typical machine learning practice, the weights and biases are initialized, then iteratively updated during training via backpropagation.
Roni Rosenfeld
Roni Rosenfeld (Hebrew: רוני רוזנפלד) is an Israeli-American computer scientist and computational epidemiologist, currently serving as the head of the Machine Learning Department at Carnegie Mellon University. He is an international expert in machine learning, infectious disease forecasting, statistical language modeling and artificial intelligence. == Education == Rosenfeld received his B.Sc. in mathematics and physics from Tel Aviv University in 1985. He received his Ph.D. in computer science from Carnegie Mellon University in 1994. While a graduate student, he developed and open-sourced a statistical language-modeling toolkit to allow anyone to create statistical language models from their own corpora and experiment with and extend the toolkit's capabilities. The toolkit has been used by more than 100 NLP laboratories in more than 20 countries. Rosenfeld's Ph.D. thesis, A Maximum Entropy Approach to Adaptive Statistical Language Modeling, was advised by Raj Reddy and Xuedong Huang and won the 2001 Computer, Speech and Language award for "Most Influential Paper in the Last 5 Years." == Career == Shortly after receiving his Ph.D., Rosenfeld joined the faculty of the Carnegie Mellon School of Computer Science as an assistant professor. He was promoted to the rank of associate professor in 1999 and received tenure in 2001. In 2005 he was promoted to professor of language technologies, machine learning computer science and computational biology in the School of Computer Science at Carnegie Mellon University. Rosenfeld also holds adjunct appointments at the University of Pittsburgh School of Medicine, department of computational and systems biology. From 2002 to 2003, Rosenfeld was a visiting professor at the University of Hong Kong. Rosenfeld is the director of Carnegie Mellon's Machine Learning for Social Good (ML4SG) program. He has held educational leadership positions in a variety of programs, including the M.S. in computational finance (1997–1999), graduate computational and statistical learning (2001–2003), M.S. in machine learning (2017) and undergraduate minor in machine learning. Rosenfeld was appointed Head of Carnegie Mellon's Machine Learning Department in 2018. == Research == Rosenfeld's research interests include epidemiological forecasting, information and communication technologies for development (ICT4D), and machine learning for social good. === Epidemiological forecasting === Rosenfeld is a world expert in epidemiological forecasting. He founded and directs the Delphi research group, which has won most of the epidemiological forecasting challenges organized by the U.S. CDC and other U.S. government agencies. In December 2016, the CDC named his group the "Most Accurate Forecaster" for 2015–2016, and in October 2017, the Delphi group's two systems took the top two spots in the 2016-2017 flu forecasting challenge. The CDC recognized Rosenfeld's Delphi group at Carnegie Mellon University as having contributed the most accurate national-, regional-, and state-level influenza-like illness forecasts and national-level hospitalization forecasts to the site. In 2019, the CDC recognized forecasts provided by the Delphi group at Carnegie Mellon as having been the most accurate for five seasons in a row, and named the Delphi group an Influenza Forecasting Center of Excellence, a five-year designation that includes $3 million in research funding. Rosenfeld describes his forecasting research goal as "to make epidemiological forecasting as universally accepted and useful as weather forecasting is today." His recent work in the area has focused on selecting high value epidemiological forecasting targets (e.g. Influenza and Dengue); creating baseline forecasting methods for them; establishing metrics for measuring and tracking forecasting accuracy; estimating the limits of forecastability for each target; and identifying new sources of data that could be helpful to the forecasting goal. == Honors and awards == 2017 Joel and Ruth Spira Teaching Award 2017 CDC Influenza Forecasting Challenge "Most Accurate Forecaster" 1992 Allen Newell Medal for Research Excellence