Batch cryptography is a field of cryptology focused on the design of cryptographic protocols that perform operations—such as encryption, decryption, key exchange, and authentication—on multiple inputs simultaneously, rather than processing each input individually. Batching cryptographic operations can significantly reduce the marginal cost of handling individual inputs—a principle that was first introduced by Amos Fiat in 1989.
Percept (artificial intelligence)
A percept is the input that an intelligent agent is perceiving at any given moment. It is essentially the same concept as a percept in psychology, except that it is being perceived not by the brain but by the agent. A percept is detected by a sensor, often a camera, processed accordingly, and acted upon by an actuator. Each percept is added to a "percept sequence", which is a complete history of each percept ever detected. The agent's action at any instant point may depend on the entire percept sequence up to that particular instant point. An intelligent agent chooses how to act not only based on the current percept, but the percept sequence. The next action is chosen by the agent function, which maps every percept to an action. For example, if a camera were to record a gesture, the agent would process the percepts, calculate the corresponding spatial vectors, examine its percept history, and use the agent program (the application of the agent function) to act accordingly. == Examples == Examples of percepts include inputs from touch sensors, cameras, infrared sensors, sonar, microphones, mice, and keyboards. A percept can also be a higher-level feature of the data, such as lines, depth, objects, faces, or gestures.
XGBoost
XGBoost (eXtreme Gradient Boosting) is an open-source software library which provides a regularizing gradient boosting framework for C++, Java, Python, R, Julia, Perl, and Scala. It works on Linux, Microsoft Windows, and macOS. From the project description, it aims to provide a "Scalable, Portable and Distributed Gradient Boosting (GBM, GBRT, GBDT) Library". It runs on a single machine, as well as the distributed processing frameworks Apache Hadoop, Apache Spark, Apache Flink, and Dask. XGBoost gained much popularity and attention in the mid-2010s as the algorithm of choice for many winning teams of machine learning competitions. == History == XGBoost initially started as a research project by Tianqi Chen as part of the Distributed (Deep) Machine Learning Community (DMLC) group at the University of Washington. Initially, it began as a terminal application which could be configured using a libsvm configuration file. It became well known in the ML competition circles after its use in the winning solution of the Higgs Machine Learning Challenge. Soon after, the Python and R packages were built, and XGBoost now has package implementations for Java, Scala, Julia, Perl, and other languages. This brought the library to more developers and contributed to its popularity among the Kaggle community, where it has been used for a large number of competitions. It was soon integrated with a number of other packages making it easier to use in their respective communities. It has now been integrated with scikit-learn for Python users and with the caret package for R users. It can also be integrated into Data Flow frameworks like Apache Spark, Apache Hadoop, and Apache Flink using the abstracted Rabit and XGBoost4J. XGBoost is also available on OpenCL for FPGAs. An efficient, scalable implementation of XGBoost has been published by Tianqi Chen and Carlos Guestrin. While the XGBoost model often achieves higher accuracy than a single decision tree, it sacrifices the intrinsic interpretability of decision trees. For example, following the path that a decision tree takes to make its decision is trivial and self-explained, but following the paths of hundreds or thousands of trees is much harder. == Features == Salient features of XGBoost which make it different from other gradient boosting algorithms include: Clever penalization of trees A proportional shrinking of leaf nodes Newton Boosting Extra randomization parameter Implementation on single, distributed systems and out-of-core computation Automatic feature selection Theoretically justified weighted quantile sketching for efficient computation Parallel tree structure boosting with sparsity Efficient cacheable block structure for decision tree training == The algorithm == XGBoost works as Newton–Raphson in function space unlike gradient boosting that works as gradient descent in function space, a second order Taylor approximation is used in the loss function to make the connection to Newton–Raphson method. A generic unregularized XGBoost algorithm is: == Parameters == XGBoost has parameters which can be specified to affect how it functions and performs. Some parameters include: Learning rate (also known as the "step size" or “"shrinkage"), it is a number between 0 and 1 (default is 0.3), which determines the rate the algorithm learns from each iteration. n_estimators, sets the number of trees to be built in the ensemble, where more trees generally increases the complexity of the model, but can lead to overfitting with too many trees. Gamma (also known as Lagrange multiplier or the minimum loss reduction parameter), controls the minimum amount of loss reduction required to make a further split on a leaf node of the tree. The default in XGBoost is 0 . max_depth, represents how deeply each tree in the boosting process can grow during training, where the default is 6. == Awards == John Chambers Award (2016) High Energy Physics meets Machine Learning award (HEP meets ML) (2016)
Stress majorization
Stress majorization is an optimization strategy used in multidimensional scaling (MDS) where, for a set of n {\displaystyle n} m {\displaystyle m} -dimensional data items, a configuration X {\displaystyle X} of n {\displaystyle n} points in r {\displaystyle r} ( ≪ m ) {\displaystyle (\ll m)} -dimensional space is sought that minimizes the so-called stress function σ ( X ) {\displaystyle \sigma (X)} . Usually r {\displaystyle r} is 2 {\displaystyle 2} or 3 {\displaystyle 3} , i.e. the ( n × r ) {\displaystyle (n\times r)} matrix X {\displaystyle X} lists points in 2 − {\displaystyle 2-} or 3 − {\displaystyle 3-} dimensional Euclidean space so that the result may be visualised (i.e. an MDS plot). The function σ {\displaystyle \sigma } is a cost or loss function that measures the squared differences between ideal ( m {\displaystyle m} -dimensional) distances and actual distances in r-dimensional space. It is defined as: σ ( X ) = ∑ i < j ≤ n w i j ( d i j ( X ) − δ i j ) 2 {\displaystyle \sigma (X)=\sum _{i Elastic maps provide a tool for nonlinear dimensionality reduction. By their construction, they are a system of elastic springs embedded in the data space. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured k-means clustering (zero elasticity) to the estimators located closely to linear PCA manifolds (for high bending and low stretching modules). With some intermediate values of the elasticity coefficients, this system effectively approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through "the middle" of the data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and A.A. Pitenko in 1996–1998. == Energy of elastic map == Let S {\displaystyle {\mathcal {S}}} be a data set in a finite-dimensional Euclidean space. Elastic map is represented by a set of nodes w j {\displaystyle {\bf {w}}_{j}} in the same space. Each datapoint s ∈ S {\displaystyle s\in {\mathcal {S}}} has a host node, namely the closest node w j {\displaystyle {\bf {w}}_{j}} (if there are several closest nodes then one takes the node with the smallest number). The data set S {\displaystyle {\mathcal {S}}} is divided into classes K j = { s | w j is a host of s } {\displaystyle K_{j}=\{s\ |\ {\bf {w}}_{j}{\mbox{ is a host of }}s\}} . The approximation energy D is the distortion D = 1 2 ∑ j = 1 k ∑ s ∈ K j ‖ s − w j ‖ 2 {\displaystyle D={\frac {1}{2}}\sum _{j=1}^{k}\sum _{s\in K_{j}}\|s-{\bf {w}}_{j}\|^{2}} , which is the energy of the springs with unit elasticity which connect each data point with its host node. It is possible to apply weighting factors to the terms of this sum, for example to reflect the standard deviation of the probability density function of any subset of data points { s i } {\displaystyle \{s_{i}\}} . On the set of nodes an additional structure is defined. Some pairs of nodes, ( w i , w j ) {\displaystyle ({\bf {w}}_{i},{\bf {w}}_{j})} , are connected by elastic edges. Call this set of pairs E {\displaystyle E} . Some triplets of nodes, ( w i , w j , w k ) {\displaystyle ({\bf {w}}_{i},{\bf {w}}_{j},{\bf {w}}_{k})} , form bending ribs. Call this set of triplets G {\displaystyle G} . The stretching energy is U E = 1 2 λ ∑ ( w i , w j ) ∈ E ‖ w i − w j ‖ 2 {\displaystyle U_{E}={\frac {1}{2}}\lambda \sum _{({\bf {w}}_{i},{\bf {w}}_{j})\in E}\|{\bf {w}}_{i}-{\bf {w}}_{j}\|^{2}} , The bending energy is U G = 1 2 μ ∑ ( w i , w j , w k ) ∈ G ‖ w i − 2 w j + w k ‖ 2 {\displaystyle U_{G}={\frac {1}{2}}\mu \sum _{({\bf {w}}_{i},{\bf {w}}_{j},{\bf {w}}_{k})\in G}\|{\bf {w}}_{i}-2{\bf {w}}_{j}+{\bf {w}}_{k}\|^{2}} , where λ {\displaystyle \lambda } and μ {\displaystyle \mu } are the stretching and bending moduli respectively. The stretching energy is sometimes referred to as the membrane, while the bending energy is referred to as the thin plate term. For example, on the 2D rectangular grid the elastic edges are just vertical and horizontal edges (pairs of closest vertices) and the bending ribs are the vertical or horizontal triplets of consecutive (closest) vertices. The total energy of the elastic map is thus U = D + U E + U G . {\displaystyle U=D+U_{E}+U_{G}.} The position of the nodes { w j } {\displaystyle \{{\bf {w}}_{j}\}} is determined by the mechanical equilibrium of the elastic map, i.e. its location is such that it minimizes the total energy U {\displaystyle U} . == Expectation-maximization algorithm == For a given splitting of dataset S {\displaystyle {\mathcal {S}}} in classes K j {\displaystyle K_{j}} , minimization of the quadratic functional U {\displaystyle U} is a linear problem with the sparse matrix of coefficients. Therefore, similar to principal component analysis or k-means, a splitting method is used: For given { w j } {\displaystyle \{{\bf {w}}_{j}\}} find { K j } {\displaystyle \{K_{j}\}} ; For given { K j } {\displaystyle \{K_{j}\}} minimize U {\displaystyle U} and find { w j } {\displaystyle \{{\bf {w}}_{j}\}} ; If no change, terminate. This expectation-maximization algorithm guarantees a local minimum of U {\displaystyle U} . For improving the approximation various additional methods are proposed. For example, the softening strategy is used. This strategy starts with a rigid grids (small length, small bending and large elasticity modules λ {\displaystyle \lambda } and μ {\displaystyle \mu } coefficients) and finishes with soft grids (small λ {\displaystyle \lambda } and μ {\displaystyle \mu } ). The training goes in several epochs, each epoch with its own grid rigidness. Another adaptive strategy is growing net: one starts from a small number of nodes and gradually adds new nodes. Each epoch goes with its own number of nodes. == Applications == Most important applications of the method and free software are in bioinformatics for exploratory data analysis and visualisation of multidimensional data, for data visualisation in economics, social and political sciences, as an auxiliary tool for data mapping in geographic informational systems and for visualisation of data of various nature. The method is applied in quantitative biology for reconstructing the curved surface of a tree leaf from a stack of light microscopy images. This reconstruction is used for quantifying the geodesic distances between trichomes and their patterning, which is a marker of the capability of a plant to resist to pathogenes. Recently, the method is adapted as a support tool in the decision process underlying the selection, optimization, and management of financial portfolios. The method of elastic maps has been systematically tested and compared with several machine learning methods on the applied problem of identification of the flow regime of a gas-liquid flow in a pipe. There are various regimes: Single phase water or air flow, Bubbly flow, Bubbly-slug flow, Slug flow, Slug-churn flow, Churn flow, Churn-annular flow, and Annular flow. The simplest and most common method used to identify the flow regime is visual observation. This approach is, however, subjective and unsuitable for relatively high gas and liquid flow rates. Therefore, the machine learning methods are proposed by many authors. The methods are applied to differential pressure data collected during a calibration process. The method of elastic maps provided a 2D map, where the area of each regime is represented. The comparison with some other machine learning methods is presented in Table 1 for various pipe diameters and pressure. Here, ANN stands for the backpropagation artificial neural networks, SVM stands for the support vector machine, SOM for the self-organizing maps. The hybrid technology was developed for engineering applications. In this technology, elastic maps are used in combination with Principal Component Analysis (PCA), Independent Component Analysis (ICA) and backpropagation ANN. The textbook provides a systematic comparison of elastic maps and self-organizing maps (SOMs) in applications to economic and financial decision-making. Cepstral mean and variance normalization (CMVN) is a computationally efficient normalization technique for robust speech recognition. The performance of CMVN is known to degrade for short utterances. This is due to insufficient data for parameter estimation and loss of discriminable information as all utterances are forced to have zero mean and unit variance. CMVN minimizes distortion by noise contamination for robust feature extraction by linearly transforming the cepstral coefficients to have the same segmental statistics. Cepstral Normalization has been effective in the CMU Sphinx for maintaining a high level of recognition accuracy over a wide variety of acoustical environments. == Cepstral Normalization Techniques == There are multiple algorithms that achieve Cepstral Normalization in different ways. === Fixed codeword-dependent cepstral normalization (FCDCN) === FCDCN was developed to provide a form of compensation that provides greater recognition accuracy than SDCN but in a more computationally-efficient manner than the CDCN algorithm. The FCDCN algorithm applies an additive correction that depends on the instantaneous SNR of the input (like SDCN), but that can also vary from codeword to codeword (like CDCN). === Multiple Fixed Codeword-dependent Cepstral Normalization (MFCDCN) === MFCDCN is a simple extension of FCDCN algorithm that does not need environment specific training. In MFCDCN, compensation vectors are pre-computed in parallel for a set of target environments, using the FCDCN algorithm. === Incremental Multiple Fixed Codeword-dependent Cepstral Normalization (IMFCDCN) === While environment selection for the compensation vectors of MFCDCN is generally performed on an utterance-by-utterance basis, IMFCFCN improves on it by allowing the classification process to make use of cepstral vectors from previous utterances in a given session. == Cepstral Noise Subtraction == Automatic speech recognition (ASR) describes the steps of transcribing speech utterances represented as acoustic wave forms to written words. As is, CMVN has been used in different applications as this technique has proven to provide better speech recognitions results in different environments. CMVN has the capabilities to reduce differences between test and training data produced by channel distortions and colorizations . CMVN has also been found to be able to reduce differences in feature representation between speakers can also partly reduce the influence of background noise. Genotypic and phenotypic repair are optional components of an evolutionary algorithm (EA). An EA reproduces essential elements of biological evolution as a computer algorithm in order to solve demanding optimization or planning tasks, at least approximately. A candidate solution is represented by a - usually linear - data structure that plays the role of an individual's chromosome. New solution candidates are generated by mutation and crossover operators following the example of biology. These offspring may be defective, which is corrected or compensated for by genotypic or phenotypic repair. == Description == Genotypic repair, also known as genetic repair, is the removal or correction of impermissible entries in the chromosome that violate restrictions. In phenotypic repair, the corrections are only made in the genotype-phenotype mapping and the chromosome remains unchanged. Michalewicz wrote about the importance of restrictions in real-world applications: "In general, constraints are an integral part of the formulation of any problem". Restriction violations are application-specific and therefore it depends on the current problem whether and which type of repair is useful. They can usually also be treated by a correspondingly extended evaluation and it depends on the problem which measures are possible and which is the most suitable. If a phenotypic repair is feasible, then it is usually the most efficient compared to the other measures. A survey on repair methods used as constraint handling techniques can be found in. Violations of the range limits of genes should be avoided as far as possible by the formulation of the genome. If this is not possible or if restrictions within the search space defined by the genome are involved, their violations are usually handled by the evaluation. This can be done, for example, by penalty functions that lower the fitness. Repair is often also required for combinatorial tasks. The application of a 1- or n-point crossover operator can, for example, lead to genes being missing in one of the child genomes that are present in duplicate in the other. In this case, a suitable genotypic repair measure is to move the surplus genes to the other genome in a positional manner. The use of the aforementioned operators in combinatorial tasks has also proven to be useful in combination with crossover types specially developed for permutations, at least for certain problems. Particularly in combinatorial problems, it has been observed that genotypic repair can promote premature convergence to a suboptimum, but can also significantly accelerate a successful search. Studies on various tasks have shown that this is application-dependent. An effective measure to avoid premature convergence is generally the use of structured populations instead of the usual panmictic ones. Sequence restrictions play a role in many scheduling tasks, for example when it comes to planning workflows. If, for example, it is specified that step A must be carried out before step B and the gene of step B is located before the gene of A in the chromosome, then there is an impermissible gene sequence. This is because the scheduling operation of step B requires the planned end of step A for correct scheduling, but this is not yet scheduled at the time gene B is processed. The problem can be solved in two ways: The scheduling operation of step B is postponed until the gene from step A has been processed. The genome remains unchanged and the repair only influences the genotype-phenotype mapping. Since only the phenotype is changed, this is referred to as phenotypic repair. If, on the other hand, the gene of step B is moved behind the gene of step A, this is a genotypic repair. The same applies to the alternative shift of gene A in front of gene B. In this case, genotypic repair has the disadvantage that it prevents a meaningful restructuring of the gene sequence in the chromosome if this requires several intermediate steps (mutations) that at least partially violate restrictions.Elastic map
Cepstral mean and variance normalization
Genotypic and phenotypic repair