In statistics, jackknife variance estimates for random forest are a way to estimate the variance in random forest models, in order to eliminate the bootstrap effects. == Jackknife variance estimates == The sampling variance of bagged learners is: V ( x ) = V a r [ θ ^ ∞ ( x ) ] {\displaystyle V(x)=Var[{\hat {\theta }}^{\infty }(x)]} Jackknife estimates can be considered to eliminate the bootstrap effects. The jackknife variance estimator is defined as: V ^ j = n − 1 n ∑ i = 1 n ( θ ^ ( − i ) − θ ¯ ) 2 {\displaystyle {\hat {V}}_{j}={\frac {n-1}{n}}\sum _{i=1}^{n}({\hat {\theta }}_{(-i)}-{\overline {\theta }})^{2}} In some classification problems, when random forest is used to fit models, jackknife estimated variance is defined as: V ^ j = n − 1 n ∑ i = 1 n ( t ¯ ( − i ) ⋆ ( x ) − t ¯ ⋆ ( x ) ) 2 {\displaystyle {\hat {V}}_{j}={\frac {n-1}{n}}\sum _{i=1}^{n}({\overline {t}}_{(-i)}^{\star }(x)-{\overline {t}}^{\star }(x))^{2}} Here, t ⋆ {\displaystyle t^{\star }} denotes a decision tree after training, t ( − i ) ⋆ {\displaystyle t_{(-i)}^{\star }} denotes the result based on samples without i t h {\displaystyle ith} observation. == Examples == E-mail spam problem is a common classification problem, in this problem, 57 features are used to classify spam e-mail and non-spam e-mail. Applying IJ-U variance formula to evaluate the accuracy of models with m=15,19 and 57. The results shows in paper( Confidence Intervals for Random Forests: The jackknife and the Infinitesimal Jackknife ) that m = 57 random forest appears to be quite unstable, while predictions made by m=5 random forest appear to be quite stable, this results is corresponding to the evaluation made by error percentage, in which the accuracy of model with m=5 is high and m=57 is low. Here, accuracy is measured by error rate, which is defined as: E r r o r R a t e = 1 N ∑ i = 1 N ∑ j = 1 M y i j , {\displaystyle ErrorRate={\frac {1}{N}}\sum _{i=1}^{N}\sum _{j=1}^{M}y_{ij},} Here N is also the number of samples, M is the number of classes, y i j {\displaystyle y_{ij}} is the indicator function which equals 1 when i t h {\displaystyle ith} observation is in class j, equals 0 when in other classes. No probability is considered here. There is another method which is similar to error rate to measure accuracy: l o g l o s s = 1 N ∑ i = 1 N ∑ j = 1 M y i j l o g ( p i j ) {\displaystyle logloss={\frac {1}{N}}\sum _{i=1}^{N}\sum _{j=1}^{M}y_{ij}log(p_{ij})} Here N is the number of samples, M is the number of classes, y i j {\displaystyle y_{ij}} is the indicator function which equals 1 when i t h {\displaystyle ith} observation is in class j, equals 0 when in other classes. p i j {\displaystyle p_{ij}} is the predicted probability of i t h {\displaystyle ith} observation in class j {\displaystyle j} .This method is used in Kaggle These two methods are very similar. == Modification for bias == When using Monte Carlo MSEs for estimating V I J ∞ {\displaystyle V_{IJ}^{\infty }} and V J ∞ {\displaystyle V_{J}^{\infty }} , a problem about the Monte Carlo bias should be considered, especially when n is large, the bias is getting large: E [ V ^ I J B ] − V ^ I J ∞ ≈ n ∑ b = 1 B ( t b ⋆ − t ¯ ⋆ ) 2 B {\displaystyle E[{\hat {V}}_{IJ}^{B}]-{\hat {V}}_{IJ}^{\infty }\approx {\frac {n\sum _{b=1}^{B}(t_{b}^{\star }-{\bar {t}}^{\star })^{2}}{B}}} To eliminate this influence, bias-corrected modifications are suggested: V ^ I J − U B = V ^ I J B − n ∑ b = 1 B ( t b ⋆ − t ¯ ⋆ ) 2 B {\displaystyle {\hat {V}}_{IJ-U}^{B}={\hat {V}}_{IJ}^{B}-{\frac {n\sum _{b=1}^{B}(t_{b}^{\star }-{\bar {t}}^{\star })^{2}}{B}}} V ^ J − U B = V ^ J B − ( e − 1 ) n ∑ b = 1 B ( t b ⋆ − t ¯ ⋆ ) 2 B {\displaystyle {\hat {V}}_{J-U}^{B}={\hat {V}}_{J}^{B}-(e-1){\frac {n\sum _{b=1}^{B}(t_{b}^{\star }-{\bar {t}}^{\star })^{2}}{B}}}
PDE surface
PDE surfaces are used in geometric modelling and computer graphics for creating smooth surfaces conforming to a given boundary configuration. PDE surfaces use partial differential equations to generate a surface which usually satisfy a mathematical boundary value problem. PDE surfaces were first introduced into the area of geometric modelling and computer graphics by two British mathematicians, Malcolm Bloor and Michael Wilson. == Technical details == The PDE method involves generating a surface for some boundary by means of solving an elliptic partial differential equation of the form ( ∂ 2 ∂ u 2 + a 2 ∂ 2 ∂ v 2 ) 2 X ( u , v ) = 0. {\displaystyle \left({\frac {\partial ^{2}}{\partial u^{2}}}+a^{2}{\frac {\partial ^{2}}{\partial v^{2}}}\right)^{2}X(u,v)=0.} Here X ( u , v ) {\displaystyle X(u,v)} is a function parameterised by the two parameters u {\displaystyle u} and v {\displaystyle v} such that X ( u , v ) = ( x ( u , v ) , y ( u , v ) , z ( u , v ) ) {\displaystyle X(u,v)=(x(u,v),y(u,v),z(u,v))} where x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} are the usual cartesian coordinate space. The boundary conditions on the function X ( u , v ) {\displaystyle X(u,v)} and its normal derivatives ∂ X / ∂ n {\displaystyle \partial {X}/\partial {n}} are imposed at the edges of the surface patch. With the above formulation it is notable that the elliptic partial differential operator in the above PDE represents a smoothing process in which the value of the function at any point on the surface is, in some sense, a weighted average of the surrounding values. In this way, a surface is obtained as a smooth transition between the chosen set of boundary conditions. The parameter a {\displaystyle a} is a special design parameter which controls the relative smoothing of the surface in the u {\displaystyle u} and v {\displaystyle v} directions. When a = 1 {\displaystyle a=1} , the PDE is the biharmonic equation: X u u u u + 2 X u u v v + X v v v v = 0 {\displaystyle X_{uuuu}+2X_{uuvv}+X_{vvvv}=0} . The biharmonic equation is the equation produced by applying the Euler-Lagrange equation to the simplified thin plate energy functional X u u 2 + 2 X u v 2 + X v v 2 {\displaystyle X_{uu}^{2}+2X_{uv}^{2}+X_{vv}^{2}} . So solving the PDE with a = 1 {\displaystyle a=1} is equivalent to minimizing the thin plate energy functional subject to the same boundary conditions. == Applications == PDE surfaces can be used in many application areas. These include computer-aided design, interactive design, parametric design, computer animation, computer-aided physical analysis and design optimisation. == Related publications == M.I.G. Bloor and M.J. Wilson, Generating Blend Surfaces using Partial Differential Equations, Computer Aided Design, 21(3), 165–171, (1989). H. Ugail, M.I.G. Bloor, and M.J. Wilson, Techniques for Interactive Design Using the PDE Method, ACM Transactions on Graphics, 18(2), 195–212, (1999). J. Huband, W. Li and R. Smith, An Explicit Representation of Bloor-Wilson PDE Surface Model by using Canonical Basis for Hermite Interpolation, Mathematical Engineering in Industry, 7(4), 421-33 (1999). H. Du and H. Qin, Direct Manipulation and Interactive Sculpting of PDE surfaces, Computer Graphics Forum, 19(3), C261-C270, (2000). H. Ugail, Spine Based Shape Parameterisations for PDE surfaces, Computing, 72, 195–204, (2004). L. You, P. Comninos, J.J. Zhang, PDE Blending Surfaces with C2 Continuity, Computers and Graphics, 28(6), 895–906, (2004).
Neural radiance field
A neural radiance field (NeRF) is a neural field for reconstructing a three-dimensional representation of a scene from two-dimensional images. The NeRF model enables downstream applications of novel view synthesis, scene geometry reconstruction, and obtaining the reflectance properties of the scene. Additional scene properties such as camera poses may also be jointly learned. First introduced in 2020, it has since gained significant attention for its potential applications in computer graphics and content creation. == Algorithm == The NeRF algorithm represents a scene as a radiance field parametrized by a deep neural network (DNN). The network predicts a volume density and view-dependent emitted radiance given the spatial location ( x , y , z ) {\displaystyle (x,y,z)} and viewing direction in Euler angles ( θ , Φ ) {\displaystyle (\theta ,\Phi )} of the camera. By sampling many points along camera rays, traditional volume rendering techniques can produce an image. === Data collection === A NeRF needs to be retrained for each unique scene. The first step is to collect images of the scene from different angles and their respective camera pose. These images are standard 2D images and do not require a specialized camera or software. Any camera is able to generate datasets, provided the settings and capture method meet the requirements for SfM (Structure from Motion). This requires tracking of the camera position and orientation, often through some combination of SLAM, GPS, or inertial estimation. Researchers often use synthetic data to evaluate NeRF and related techniques. For such data, images (rendered through traditional non-learned methods) and respective camera poses are reproducible and error-free. === Training === For each sparse viewpoint (image and camera pose) provided, camera rays are marched through the scene, generating a set of 3D points with a given radiance direction (into the camera). For these points, volume density and emitted radiance are predicted using the multi-layer perceptron (MLP). An image is then generated through classical volume rendering. Because this process is fully differentiable, the error between the predicted image and the original image can be minimized with gradient descent over multiple viewpoints, encouraging the MLP to develop a coherent model of the scene. == Variations and improvements == Early versions of NeRF were slow to optimize and required that all input views were taken with the same camera in the same lighting conditions. These performed best when limited to orbiting around individual objects, such as a drum set, plants or small toys. Since the original paper in 2020, many improvements have been made to the NeRF algorithm, with variations for special use cases. === Fourier feature mapping === In 2020, shortly after the release of NeRF, the addition of Fourier Feature Mapping improved training speed and image accuracy. Deep neural networks struggle to learn high frequency functions in low dimensional domains; a phenomenon known as spectral bias. To overcome this shortcoming, points are mapped to a higher dimensional feature space before being fed into the MLP. γ ( v ) = [ a 1 cos ( 2 π B 1 T v ) a 1 sin ( 2 π B 1 T v ) ⋮ a m cos ( 2 π B m T v ) a m sin ( 2 π B m T v ) ] {\displaystyle \gamma (\mathrm {v} )={\begin{bmatrix}a_{1}\cos(2{\pi }{\mathrm {B} }_{1}^{T}\mathrm {v} )\\a_{1}\sin(2\pi {\mathrm {B} }_{1}^{T}\mathrm {v} )\\\vdots \\a_{m}\cos(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\\a_{m}\sin(2{\pi }{\mathrm {B} }_{m}^{T}\mathrm {v} )\end{bmatrix}}} Where v {\displaystyle \mathrm {v} } is the input point, B i {\displaystyle \mathrm {B} _{i}} are the frequency vectors, and a i {\displaystyle a_{i}} are coefficients. This allows for rapid convergence to high frequency functions, such as pixels in a detailed image. === Bundle-adjusting neural radiance fields === One limitation of NeRFs is the requirement of knowing accurate camera poses to train the model. Often times, pose estimation methods are not completely accurate, nor is the camera pose even possible to know. These imperfections result in artifacts and suboptimal convergence. So, a method was developed to optimize the camera pose along with the volumetric function itself. Called Bundle-Adjusting Neural Radiance Field (BARF), the technique uses a dynamic low-pass filter (DLPF) to go from coarse to fine adjustment, minimizing error by finding the geometric transformation to the desired image. This corrects imperfect camera poses and greatly improves the quality of NeRF renders. === Multiscale representation === Conventional NeRFs struggle to represent detail at all viewing distances, producing blurry images up close and overly aliased images from distant views. In 2021, researchers introduced a technique to improve the sharpness of details at different viewing scales known as mip-NeRF (comes from mipmap). Rather than sampling a single ray per pixel, the technique fits a gaussian to the conical frustum cast by the camera. This improvement effectively anti-aliases across all viewing scales. mip-NeRF also reduces overall image error and is faster to converge at about half the size of ray-based NeRF. === Learned initializations === In 2021, researchers applied meta-learning to assign initial weights to the MLP. This rapidly speeds up convergence by effectively giving the network a head start in gradient descent. Meta-learning also allowed the MLP to learn an underlying representation of certain scene types. For example, given a dataset of famous tourist landmarks, an initialized NeRF could partially reconstruct a scene given one image. === NeRF in the wild === Conventional NeRFs are vulnerable to slight variations in input images (objects, lighting) often resulting in ghosting and artifacts. As a result, NeRFs struggle to represent dynamic scenes, such as bustling city streets with changes in lighting and dynamic objects. In 2021, researchers at Google developed a new method for accounting for these variations, named NeRF in the Wild (NeRF-W). This method splits the neural network (MLP) into three separate models. The main MLP is retained to encode the static volumetric radiance. However, it operates in sequence with a separate MLP for appearance embedding (changes in lighting, camera properties) and an MLP for transient embedding (changes in scene objects). This allows the NeRF to be trained on diverse photo collections, such as those taken by mobile phones at different times of day. === Relighting === In 2021, researchers added more outputs to the MLP at the heart of NeRFs. The output now included: volume density, surface normal, material parameters, distance to the first surface intersection (in any direction), and visibility of the external environment in any direction. The inclusion of these new parameters lets the MLP learn material properties, rather than pure radiance values. This facilitates a more complex rendering pipeline, calculating direct and global illumination, specular highlights, and shadows. As a result, the NeRF can render the scene under any lighting conditions with no re-training. === Plenoctrees === Although NeRFs had reached high levels of fidelity, their costly compute time made them useless for many applications requiring real-time rendering, such as VR/AR and interactive content. Introduced in 2021, Plenoctrees (plenoptic octrees) enabled real-time rendering of pre-trained NeRFs through division of the volumetric radiance function into an octree. Rather than assigning a radiance direction into the camera, viewing direction is taken out of the network input and spherical radiance is predicted for each region. This makes rendering over 3000x faster than conventional NeRFs. === Sparse Neural Radiance Grid === Similar to Plenoctrees, this method enabled real-time rendering of pretrained NeRFs. To avoid querying the large MLP for each point, this method bakes NeRFs into Sparse Neural Radiance Grids (SNeRG). A SNeRG is a sparse voxel grid containing opacity and color, with learned feature vectors to encode view-dependent information. A lightweight, more efficient MLP is then used to produce view-dependent residuals to modify the color and opacity. To enable this compressive baking, small changes to the NeRF architecture were made, such as running the MLP once per pixel rather than for each point along the ray. These improvements make SNeRG extremely efficient, outperforming Plenoctrees. === Instant NeRFs === In 2022, researchers at Nvidia enabled real-time training of NeRFs through a technique known as Instant Neural Graphics Primitives. An innovative input encoding reduces computation, enabling real-time training of a NeRF, an improvement orders of magnitude above previous methods. The speedup stems from the use of spatial hash functions, which have O ( 1 ) {\displaystyle O(1)} access times, and parallelized architectures which run fast on modern GPUs. == Related techniques == === Plenoxels === Plen
Amazon Q
Amazon Q is a chatbot developed by Amazon for enterprise use. Based on both Amazon Titan and GPT-5, it was announced on November 28, 2023. At launch, it was a part of the Amazon Web Services management console. Amazon CodeWhisperer is a part of Amazon Q Developer, a part of Amazon Q. == History == Amazon's business-focused chatbot Q was announced on November 28, 2023 in a preview, with a full version available at $20 per person per month. On July 19, 2025, the Amazon Q Visual Studio Code extension was compromised to delete the user's home directory. The issue was fixed on July 21. == Capabilities == Q can be prompted to summarize long documents and group chats, create charts, data analysis and write code. Q is also capable of accessing non-Amazon services. The chatbot is based on Amazon Titan and GPT-5, and uses the Amazon Bedrock repository of foundational models. It is part of the Amazon Web Services management console.
INDECT
INDECT is a research project in the area of intelligent security systems performed by several European universities since 2009 and funded by the European Union. The purpose of the project is to involve European scientists and researchers in the development of solutions to and tools for automatic threat detection through e.g. processing of CCTV camera data streams, standardization of video sequence quality for user applications, threat detection in computer networks as well as data and privacy protection. The area of research, applied methods, and techniques are described in the public deliverables which are available to the public on the project's website. Practically, all information related to the research is public. Only documents that comprise information related to financial data or information that could negatively influence the competitiveness and law enforcement capabilities of parties involved in the project are not published. This follows regulations and practices applied in EU research projects. == Application and target users == The main end-user of INDECT solutions are police forces and security services. The principle of operation of the project is detecting threats and identifying sources of threats, without monitoring and searching for particular citizens or groups of citizens. Then, the system operator (i.e. police officer) decides whether an intervention of services responsible for public security are required or not. Further investigation eventually leading to persons related to threats is performed, preserving the presumption of innocence, based on existing procedures already used by police services and prosecutors. As it can be found in the project deliverables, INDECT does not involve storage of personal data (such as names, addresses, identity document numbers, etc.). A similar, behavior-based surveillance program was SAMURAI (Suspicious and Abnormal behavior Monitoring Using a netwoRk of cAmeras & sensors for sItuation awareness enhancement). == Expected results == The main expected results of the INDECT project are: Trial of intelligent analysis of video and audio data for threat detection in urban environments Creation of tools and technology for privacy and data protection during storage and transmission of information using quantum cryptography and new methods of digital watermarking Performing computer-aided detection of threats and targeted crimes in Internet resources with privacy-protecting solutions Construction of a search engine for rapid semantic search based on watermarking of content related to child pornography and human organ trafficking Implementation of a distributed computer system that is capable of effective intelligent processing == Controversy == Some media and other sources accuse INDECT of privacy abuse, collecting personal data, and keeping information from the public. Consequently, these issues have been commented and discussed by some Members of the European Parliament. As seen in the project's documentation, INDECT does not involve mobile phone tracking or call interception. The rumors about testing INDECT during 2012 UEFA European Football Championship also turned out to be false. The mid-term review of the Seventh Framework Programme to the European Parliament strongly urges the European Commission to immediately make all documents available and to define a clear and strict mandate for the research goal, the application, and the end users of INDECT, and stresses a thorough investigation of the possible impact on fundamental rights. Nevertheless, according to Mr. Paweł Kowal, MEP, the project had the ethical review on 15 March 2011 in Brussels with the participation of ethics experts from Austria, France, Netherlands, Germany and Great Britain.
Microsoft To Do
Microsoft To Do (previously styled as Microsoft To-Do) is a cloud-based task management application. It allows users to manage their tasks from a smartphone, tablet and computer. The technology is produced by the team behind Wunderlist, which was acquired by Microsoft, and the stand-alone apps feed into the existing Tasks feature of the Outlook product range. == History == Microsoft To Do was first launched as a preview with basic features in April 2017. Later more features were added including Task list sharing in June 2018. In September 2019, a major update to the app was unveiled, adopting a new user interface with a closer resemblance to Wunderlist. The name was also slightly updated by removing the hyphen from To-Do. In May 2020, Microsoft officially closed the doors on Wunderlist, ending its active service in favor of improving and expanding Microsoft To Do.
NetOwl
NetOwl is a suite of multilingual text and identity analytics products that analyze big data in the form of text data – reports, web, social media, etc. – as well as structured entity data about people, organizations, places, and things. NetOwl utilizes artificial intelligence (AI)-based approaches, including natural language processing (NLP), machine learning (ML), and computational linguistics, to extract entities, relationships, and events; to perform sentiment analysis; to assign latitude/longitude to geographical references in text; to translate names written in foreign languages; and to perform name matching and identity resolution. NetOwl's uses include semantic search and discovery, geospatial analysis, intelligence analysis, content enrichment, compliance monitoring, cyber threat monitoring, risk management, and bioinformatics. == History == The first NetOwl product was NetOwl Extractor, which was initially released in 1996. Since then, Extractor has added many new capabilities, including relationship and event extraction, categorization, name translation, geotagging, and sentiment analysis, as well as entity extraction in other languages. Other products were added later to the NetOwl suite, namely TextMiner, NameMatcher, and EntityMatcher. NetOwl has participated in several 3rd party-sponsored text and entity analytics software benchmarking events. NetOwl Extractor was the top-scoring named entity extraction system at the DARPA-sponsored Message Understanding Conference MUC-6 and the top-scoring link and event extraction system in MUC-7. It was also the top-scoring system at several of the NIST-sponsored Automatic Content Extraction (ACE) evaluation tasks. NetOwl NameMatcher was the top-scoring system at the MITRE Challenge for Multicultural Person Name Matching. == Products == The NetOwl suite includes, among others, the following text and entity analytics products: === Text Analytics === NetOwl Extractor performs entity extraction from unstructured texts using natural language processing (NLP), machine learning (ML), and computational linguistics. Extractor also performs semantic relationship and event extraction as well as geotagging of text. It is used for a variety of data sources including both traditional sources (e.g., news, reports, web pages, email) and social media (e.g., Twitter, Facebook, chats, blogs). It runs on a variety of Big Data analytics platforms, including Apache Hadoop and LexisNexis’s High-Performance Computer Cluster (HPCC) technology. It has been integrated with a number of 3rd party analytical tools such as Esri ArcGIS and Google Earth/Maps. === Identity Analytics === NetOwl NameMatcher and EntityMatcher perform name matching and identity resolution for large multicultural and multilingual entity databases using machine learning (ML) and computational linguistics approaches. They are used for applications such as anti–money laundering (AML), watch lists, regulatory compliance, fraud detection, etc.