The Georgetown–IBM experiment was an influential demonstration of machine translation, which was performed on January 7, 1954. Developed jointly by Georgetown University and IBM, the experiment involved completely automatic translation of more than sixty Russian sentences into English. == Background == Conceived and performed primarily in order to attract governmental and public interest and funding by showing the possibilities of machine translation, it was by no means a fully featured system: It had only six grammar rules and 250 lexical items in its vocabulary (of stems and endings). Words in the vocabulary were in the fields of politics, law, mathematics, chemistry, metallurgy, communications and military affairs. Vocabulary was punched onto punch cards. This complete dictionary was never fully shown (only the extended one from Garvin's article). Apart from general topics, the system was specialized in the domain of organic chemistry. The translation was carried out using an IBM 701 mainframe computer (launched in April 1953). The Georgetown-IBM experiment is the best-known result of the MIT conference in June 1952 to which all active researchers in the machine translation field were invited. At the conference, Duncan Harkin from US Department of Defense suggested that his department would finance a new machine translation project. Jerome Weisner supported the idea and offered finance from the Research Laboratory of Electronics at MIT. Leon Dostert had been invited to the project for his previous experience with the automatic correction of translations (back then 'mechanical translation'); his interpretation system had a strong impact on the Nuremberg War Crimes Tribunal. The linguistics part of the demonstration was carried out for the most part by linguist Paul Garvin who had also good knowledge of Russian. Over 60 Romanized Russian statements from a wide range of political, legal, mathematical, and scientific topics were entered into the machine by a computer operator who knew no Russian, and the resulting English translations appeared on a printer. The sentences to be translated were carefully selected. Many operations for the demonstration were fitted to specific words and sentences. In addition, there was no relational or sentence analysis which could recognize the sentence structure. The approach was mostly 'lexicographical' based on a dictionary where a specific word had a connection with specific rules and steps. == Algorithm == The algorithm first translates Russian words into numerical codes, then performs the following case-analysis on each numerical code to choose between possible English word translations, reorder the English words, or omit some English words. The flowchart of the algorithm is reproduced in (see Table 1 for the 6 rules). == Translation examples == How it analyzes Vyelyichyina ugla opryedyelyayetsya otnoshyenyiyem dlyini dugi k radyiusu (figure 2 of ). == Reception == Well publicized by journalists and perceived as a success, the experiment did encourage governments to invest in computational linguistics. The authors claimed that within three or five years, machine translation could well be a solved problem. However, the real progress was much slower, and after the ALPAC report in 1966, which found that the ten years of long research had failed to fulfill the expectations, funding was reduced dramatically. The demonstration was given widespread coverage in the foreign press, but only a small fraction of journalists drew attention to previous machine translation attempts.
Semantic decomposition (natural language processing)
A semantic decomposition is an algorithm that breaks down the meanings of phrases or concepts into less complex concepts. The result of a semantic decomposition is a representation of meaning. This representation can be used for tasks, such as those related to artificial intelligence or machine learning. Semantic decomposition is common in natural language processing applications. The basic idea of a semantic decomposition is taken from the learning skills of adult humans, where words are explained using other words. It is based on Meaning-text theory. Meaning-text theory is used as a theoretical linguistic framework to describe the meaning of concepts with other concepts. == Background == Given that an AI does not inherently have language, it is unable to think about the meanings behind the words of a language. An artificial notion of meaning needs to be created for a strong AI to emerge. Creating an artificial representation of meaning requires the analysis of what meaning is. Many terms are associated with meaning, including semantics, pragmatics, knowledge and understanding or word sense. Each term describes a particular aspect of meaning, and contributes to a multitude of theories explaining what meaning is. These theories need to be analyzed further to develop an artificial notion of meaning best fit for our current state of knowledge. == Graph representations == Representing meaning as a graph is one of the two ways that both an AI cognition and a linguistic researcher think about meaning (connectionist view). Logicians utilize a formal representation of meaning to build upon the idea of symbolic representation, whereas description logics describe languages and the meaning of symbols. This contention between 'neat' and 'scruffy' techniques has been discussed since the 1970s. Research has so far identified semantic measures and with that word-sense disambiguation (WSD) - the differentiation of meaning of words - as the main problem of language understanding. As an AI-complete environment, WSD is a core problem of natural language understanding. AI approaches that use knowledge-given reasoning creates a notion of meaning combining the state of the art knowledge of natural meaning with the symbolic and connectionist formalization of meaning for AI. The abstract approach is shown in Figure. First, a connectionist knowledge representation is created as a semantic network consisting of concepts and their relations to serve as the basis for the representation of meaning. This graph is built out of different knowledge sources like WordNet, Wiktionary, and BabelNET. The graph is created by lexical decomposition that recursively breaks each concept semantically down into a set of semantic primes. The primes are taken from the theory of Natural Semantic Metalanguage, which has been analyzed for usefulness in formal languages. Upon this graph marker passing is used to create the dynamic part of meaning representing thoughts. The marker passing algorithm, where symbolic information is passed along relations form one concept to another, uses node and edge interpretation to guide its markers. The node and edge interpretation model is the symbolic influence of certain concepts. Future work uses the created representation of meaning to build heuristics and evaluate them through capability matching and agent planning, chatbots or other applications of natural language understanding.
Leakage (machine learning)
In statistics and machine learning, leakage (also known as data leakage or target leakage) refers to the use of information during model training that would not be available at prediction time. This results in overly optimistic performance estimates, as the model appears to perform better during evaluation than it actually would in a production environment. Leakage is often subtle and indirect, making it difficult to detect and eliminate. It can lead a statistician or modeler to select a suboptimal model, which may be outperformed by a leakage-free alternative. == Leakage modes == Leakage can occur at multiple stages of the machine learning workflow. Broadly, its sources can be divided into two categories: those arising from features and those arising from training examples. === Feature leakage === Feature or column-wise leakage is caused by the inclusion of columns which are one of the following: a duplicate label, a proxy for the label, or the label itself. These features, known as anachronisms, will not be available when the model is used for predictions, and result in leakage if included when the model is trained. For example, including a "MonthlySalary" column when predicting "YearlySalary"; or "MinutesLate" when predicting "IsLate". === Training example leakage === Row-wise leakage is caused by improper sharing of information between rows of data. Types of row-wise leakage include: Premature featurization; leaking from premature featurization before Cross-validation/Train/Test split (must fit MinMax/ngrams/etc on only the train split, then transform the test set) Duplicate rows between train/validation/test (for example, oversampling a dataset to pad its size before splitting; or, different rotations/augmentations of a single image; bootstrap sampling before splitting; or duplicating rows to up sample the minority class) Non-independent and identically distributed random (non-IID) data Time leakage (for example, splitting a time-series dataset randomly instead of newer data in test set using a train/test split or rolling-origin cross-validation) Group leakage—not including a grouping split column (for example, Andrew Ng's group had 100k x-rays of 30k patients, meaning ~3 images per patient. The paper used random splitting instead of ensuring that all images of a patient were in the same split. Hence the model partially memorized the patients instead of learning to recognize pneumonia in chest x-rays.) A 2023 review found data leakage to be "a widespread failure mode in machine-learning (ML)-based science", having affected at least 294 academic publications across 17 disciplines, and causing a potential reproducibility crisis. == Detection == Data leakage in machine learning can be detected through various methods, focusing on performance analysis, feature examination, data auditing, and model behavior analysis. Performance-wise, unusually high accuracy or significant discrepancies between training and test results often indicate leakage. Inconsistent cross-validation outcomes may also signal issues. Feature examination involves scrutinizing feature importance rankings and ensuring temporal integrity in time series data. A thorough audit of the data pipeline is crucial, reviewing pre-processing steps, feature engineering, and data splitting processes. Detecting duplicate entries across dataset splits is also important. For language models, the Min-K% method can detect the presence of data in a pretraining dataset. It presents a sentence suspected to be present in the pretraining dataset, and computes the log-likelihood of each token, then compute the average of the lowest K of these. If this exceeds a threshold, then the sentence is likely present. This method is improved by comparing against a baseline of the mean and variance. Analyzing model behavior can reveal leakage. Models relying heavily on counter-intuitive features or showing unexpected prediction patterns warrant investigation. Performance degradation over time when tested on new data may suggest earlier inflated metrics due to leakage. Advanced techniques include backward feature elimination, where suspicious features are temporarily removed to observe performance changes. Using a separate hold-out dataset for final validation before deployment is advisable.
Hello World: How to be Human in the Age of the Machine
Hello World: How to Be Human in the Age of the Machine (also titled Hello World: Being Human in the Age of Algorithms) is a book on the growing influence of algorithms and artificial intelligence (AI) on human life, authored by mathematician and science communicator Hannah Fry. The book examines how algorithms are increasingly shaping decisions in critical areas such as healthcare, transportation, justice, finance, and the arts. == Overview == Fry uses real-world examples, such as driverless cars and predictive policing, to illustrate her points. She emphasizes that algorithms are not inherently objective; they reflect biases embedded in their design and data inputs. While acknowledging their potential to improve efficiency and accuracy, Fry cautions against over-reliance on machines without human judgment. Fry explores moral questions surrounding algorithmic decision-making, such as whether machines can replace human empathy in critical situations. She advocates for greater scrutiny of algorithms to ensure fairness and avoid harmful biases. The book proposes a "cyborg future", where humans work alongside algorithms to enhance decision-making while retaining ultimate control. == Reception == Hello World has been praised for its clarity, engaging storytelling, and balanced perspective. Critics have highlighted Fry's ability to make complex topics accessible to general audiences while raising important questions about technology's impact on society. The book was shortlisted for awards such as the 2018 Baillie Gifford Prize and the Royal Society Science Book Prize.
Energy-based model
An energy-based model (EBM), also called Canonical Ensemble Learning (CEL) or Learning via Canonical Ensemble (LCE), is an application of canonical ensemble formulation from statistical physics for learning from data. The approach prominently appears in generative artificial intelligence. EBMs provide a unified framework for many probabilistic and non-probabilistic approaches to such learning, particularly for training graphical and other structured models. An EBM learns the characteristics of a target dataset and generates a similar but larger dataset. EBMs detect the latent variables of a dataset and generate new datasets with a similar distribution. Energy-based generative neural networks is a class of generative models, which aim to learn explicit probability distributions of data in the form of energy-based models, the energy functions of which are parameterized by modern deep neural networks. Boltzmann machines are a special form of energy-based models with a specific parametrization of the energy. == Description == For a given input x {\displaystyle x} , the model describes an energy E θ ( x ) {\displaystyle E_{\theta }(x)} such that the Boltzmann distribution P θ ( x ) = e − β E θ ( x ) Z ( θ ) {\displaystyle P_{\theta }(x)={e^{-\beta E_{\theta }(x)} \over Z(\theta )}} is a probability (density), and typically β = 1 {\displaystyle \beta =1} . Since the normalization constant: Z ( θ ) := ∫ x ∈ X e − β E θ ( x ) d x {\displaystyle Z(\theta ):=\int _{x\in X}e^{-\beta E_{\theta }(x)}dx} (also known as the partition function) depends on all the Boltzmann factors of all possible inputs x {\displaystyle x} , it cannot be easily computed or reliably estimated during training simply using standard maximum likelihood estimation. However, for maximizing the likelihood during training, the gradient of the log-likelihood of a single training example x {\displaystyle x} is given by using the chain rule: ∂ θ log ( P θ ( x ) ) = E x ′ ∼ P θ [ ∂ θ E θ ( x ′ ) ] − ∂ θ E θ ( x ) ( ∗ ) {\displaystyle \partial _{\theta }\log \left(P_{\theta }(x)\right)=\mathbb {E} _{x'\sim P_{\theta }}[\partial _{\theta }E_{\theta }(x')]-\partial _{\theta }E_{\theta }(x)\,()} The expectation in the above formula for the gradient can be approximately estimated by drawing samples x ′ {\displaystyle x'} from the distribution P θ {\displaystyle P_{\theta }} using Markov chain Monte Carlo (MCMC). Early energy-based models, such as the 2003 Boltzmann machine by Hinton, estimated this expectation via blocked Gibbs sampling. Newer approaches make use of more efficient Stochastic Gradient Langevin Dynamics (LD), drawing samples using: x 0 ′ ∼ P 0 , x i + 1 ′ = x i ′ − α 2 ∂ E θ ( x i ′ ) ∂ x i ′ + ϵ {\displaystyle x_{0}'\sim P_{0},x_{i+1}'=x_{i}'-{\frac {\alpha }{2}}{\frac {\partial E_{\theta }(x_{i}')}{\partial x_{i}'}}+\epsilon } , where ϵ ∼ N ( 0 , α ) {\displaystyle \epsilon \sim {\mathcal {N}}(0,\alpha )} . A replay buffer of past values x i ′ {\displaystyle x_{i}'} is used with LD to initialize the optimization module. The parameters θ {\displaystyle \theta } of the neural network are therefore trained in a generative manner via MCMC-based maximum likelihood estimation: the learning process follows an "analysis by synthesis" scheme, where within each learning iteration, the algorithm samples the synthesized examples from the current model by a gradient-based MCMC method (e.g., Langevin dynamics or Hybrid Monte Carlo), and then updates the parameters θ {\displaystyle \theta } based on the difference between the training examples and the synthesized ones – see equation ( ∗ ) {\displaystyle ()} . This process can be interpreted as an alternating mode seeking and mode shifting process, and also has an adversarial interpretation. Essentially, the model learns a function E θ {\displaystyle E_{\theta }} that associates low energies to correct values, and higher energies to incorrect values. After training, given a converged energy model E θ {\displaystyle E_{\theta }} , the Metropolis–Hastings algorithm can be used to draw new samples. The acceptance probability is given by: P a c c ( x i → x ∗ ) = min ( 1 , P θ ( x ∗ ) P θ ( x i ) ) . {\displaystyle P_{acc}(x_{i}\to x^{})=\min \left(1,{\frac {P_{\theta }(x^{})}{P_{\theta }(x_{i})}}\right).} == History == The term "energy-based models" was first coined in a 2003 JMLR paper where the authors defined a generalisation of independent components analysis to the overcomplete setting using EBMs. Other early work on EBMs proposed models that represented energy as a composition of latent and observable variables. == Characteristics == EBMs demonstrate useful properties: Simplicity and stability. The EBM is the only object that needs to be designed and trained. Separate networks need not be trained to ensure balance. Adaptive computation time. An EBM can generate sharp, diverse samples or (more quickly) coarse, less diverse samples. Given infinite time, this procedure produces true samples. Flexibility. In Variational Autoencoders (VAE) and flow-based models, the generator learns a map from a continuous space to a (possibly) discontinuous space containing different data modes. EBMs can learn to assign low energies to disjoint regions (multiple modes). Adaptive generation. EBM generators are implicitly defined by the probability distribution, and automatically adapt as the distribution changes (without training), allowing EBMs to address domains where generator training is impractical, as well as minimizing mode collapse and avoiding spurious modes from out-of-distribution samples. Compositionality. Individual models are unnormalized probability distributions, allowing models to be combined through product of experts or other hierarchical techniques. == Experimental results == On image datasets such as CIFAR-10 and ImageNet 32x32, an EBM model generated high-quality images relatively quickly. It supported combining features learned from one type of image for generating other types of images. It was able to generalize using out-of-distribution datasets, outperforming flow-based and autoregressive models. EBM was relatively resistant to adversarial perturbations, behaving better than models explicitly trained against them with training for classification. == Applications == Target applications include natural language processing, robotics and computer vision. The first energy-based generative neural network is the generative ConvNet proposed in 2016 for image patterns, where the neural network is a convolutional neural network. The model has been generalized to various domains to learn distributions of videos, and 3D voxels. They are made more effective in their variants. They have proven useful for data generation (e.g., image synthesis, video synthesis, 3D shape synthesis, etc.), data recovery (e.g., recovering videos with missing pixels or image frames, 3D super-resolution, etc), data reconstruction (e.g., image reconstruction and linear interpolation ). == Alternatives == EBMs compete with techniques such as variational autoencoders (VAEs), generative adversarial networks (GANs) or normalizing flows. == Extensions == === Joint energy-based models === Joint energy-based models (JEM), proposed in 2020 by Grathwohl et al., allow any classifier with softmax output to be interpreted as energy-based model. The key observation is that such a classifier is trained to predict the conditional probability p θ ( y | x ) = e f → θ ( x ) [ y ] ∑ j = 1 K e f → θ ( x ) [ j ] for y = 1 , … , K and f → θ = ( f 1 , … , f K ) ∈ R K , {\displaystyle p_{\theta }(y|x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{\sum _{j=1}^{K}e^{{\vec {f}}_{\theta }(x)[j]}}}\ \ {\text{ for }}y=1,\dotsc ,K{\text{ and }}{\vec {f}}_{\theta }=(f_{1},\dotsc ,f_{K})\in \mathbb {R} ^{K},} where f → θ ( x ) [ y ] {\displaystyle {\vec {f}}_{\theta }(x)[y]} is the y-th index of the logits f → {\displaystyle {\vec {f}}} corresponding to class y. Without any change to the logits it was proposed to reinterpret the logits to describe a joint probability density: p θ ( y , x ) = e f → θ ( x ) [ y ] Z ( θ ) , {\displaystyle p_{\theta }(y,x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}},} with unknown partition function Z ( θ ) {\displaystyle Z(\theta )} and energy E θ ( x , y ) = − f θ ( x ) [ y ] {\displaystyle E_{\theta }(x,y)=-f_{\theta }(x)[y]} . By marginalization, we obtain the unnormalized density p θ ( x ) = ∑ y p θ ( y , x ) = ∑ y e f → θ ( x ) [ y ] Z ( θ ) =: e − E θ ( x ) , {\displaystyle p_{\theta }(x)=\sum _{y}p_{\theta }(y,x)=\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}=:e^{-E_{\theta }(x)},} therefore, E θ ( x ) = − log ( ∑ y e f → θ ( x ) [ y ] Z ( θ ) ) , {\displaystyle E_{\theta }(x)=-\log \left(\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}\right),} so that any classifier can be used to define an energy function E θ ( x ) {\displaystyle E_{\theta }(x)} .
Supermind AI
Supermind is a state-funded Chinese artificial intelligence platform that tracks scientists and researchers internationally. The platform is the flagship project of Shenzhen's International Science and Technology Information Center. It mines data from science and technology databases such as Springer, Wiley, Clarivate and Elsevier. It is intended to detect technological breakthroughs and to identify possible sources of talent as part of China's efforts to advance technologically. The platform also uses government data security and security intelligence organizations such as Peng Cheng Laboratory, the China National GeneBank, BGI Group and the Key Laboratory of New Technologies of Security Intelligence. According to Hong Kong-based Asia Times, the platform, "While not an overt espionage tool...may be used to identify key personnel who could be bribed, deceived or manipulated into divulging classified information". The Organisation for Economic Co-operation and Development (OECD) flagged the project as an incident, meaning it may be of interest to policymakers and other stakeholders. US technology group American Edge Project criticized the project as a global risk of China's security services using the platform to place agents in jobs with access to important information, recruit technical personnel, and identify targets for hacking operations.
Conditional random field
Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. The kind of graph used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions. Other examples where CRFs are used are: labeling or parsing of sequential data for natural language processing or biological sequences, part-of-speech tagging, shallow parsing, named entity recognition, gene finding, peptide critical functional region finding, and object recognition and image segmentation in computer vision. == Description == CRFs are a type of discriminative undirected probabilistic graphical model. Lafferty, McCallum and Pereira define a CRF on observations X {\displaystyle {\boldsymbol {X}}} and random variables Y {\displaystyle {\boldsymbol {Y}}} as follows: Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph such that Y = ( Y v ) v ∈ V {\displaystyle {\boldsymbol {Y}}=({\boldsymbol {Y}}_{v})_{v\in V}} , so that Y {\displaystyle {\boldsymbol {Y}}} is indexed by the vertices of G {\displaystyle G} . Then ( X , Y ) {\displaystyle ({\boldsymbol {X}},{\boldsymbol {Y}})} is a conditional random field when each random variable Y v {\displaystyle {\boldsymbol {Y}}_{v}} , conditioned on X {\displaystyle {\boldsymbol {X}}} , obeys the Markov property with respect to the graph; that is, its probability is dependent only on its neighbours in G and not its past states: P ( Y v | X , { Y w : w ≠ v } ) = P ( Y v | X , { Y w : w ∼ v } ) {\displaystyle P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\neq v\})=P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\sim v\})} , where w ∼ v {\displaystyle {\mathit {w}}\sim v} means that w {\displaystyle w} and v {\displaystyle v} are neighbors in G {\displaystyle G} . What this means is that a CRF is an undirected graphical model whose nodes can be divided into exactly two disjoint sets X {\displaystyle {\boldsymbol {X}}} and Y {\displaystyle {\boldsymbol {Y}}} , the observed and output variables, respectively; the conditional distribution p ( Y | X ) {\displaystyle p({\boldsymbol {Y}}|{\boldsymbol {X}})} is then modeled. === Inference === For general graphs, the problem of exact inference in CRFs is intractable. The inference problem for a CRF is basically the same as for an MRF and the same arguments hold. However, there exist special cases for which exact inference is feasible: If the graph is a chain or a tree, message passing algorithms yield exact solutions. The algorithms used in these cases are analogous to the forward-backward and Viterbi algorithm for the case of HMMs. If the CRF only contains pair-wise potentials and the energy is submodular, combinatorial min cut/max flow algorithms yield exact solutions. If exact inference is impossible, several algorithms can be used to obtain approximate solutions. These include: Loopy belief propagation Alpha expansion Mean field inference Linear programming relaxations === Parameter learning === Learning the parameters θ {\displaystyle \theta } is usually done by maximum likelihood learning for p ( Y i | X i ; θ ) {\displaystyle p(Y_{i}|X_{i};\theta )} . If all nodes have exponential family distributions and all nodes are observed during training, this optimization is convex. It can be solved for example using gradient descent algorithms, or Quasi-Newton methods such as the L-BFGS algorithm. On the other hand, if some variables are unobserved, the inference problem has to be solved for these variables. Exact inference is intractable in general graphs, so approximations have to be used. === Examples === In sequence modeling, the graph of interest is usually a chain graph. An input sequence of observed variables X {\displaystyle X} represents a sequence of observations and Y {\displaystyle Y} represents a hidden (or unknown) state variable that needs to be inferred given the observations. The Y i {\displaystyle Y_{i}} are structured to form a chain, with an edge between each Y i − 1 {\displaystyle Y_{i-1}} and Y i {\displaystyle Y_{i}} . As well as having a simple interpretation of the Y i {\displaystyle Y_{i}} as "labels" for each element in the input sequence, this layout admits efficient algorithms for: model training, learning the conditional distributions between the Y i {\displaystyle Y_{i}} and feature functions from some corpus of training data. decoding, determining the probability of a given label sequence Y {\displaystyle Y} given X {\displaystyle X} . inference, determining the most likely label sequence Y {\displaystyle Y} given X {\displaystyle X} . The conditional dependency of each Y i {\displaystyle Y_{i}} on X {\displaystyle X} is defined through a fixed set of feature functions of the form f ( i , Y i − 1 , Y i , X ) {\displaystyle f(i,Y_{i-1},Y_{i},X)} , which can be thought of as measurements on the input sequence that partially determine the likelihood of each possible value for Y i {\displaystyle Y_{i}} . The model assigns each feature a numerical weight and combines them to determine the probability of a certain value for Y i {\displaystyle Y_{i}} . Linear-chain CRFs have many of the same applications as conceptually simpler hidden Markov models (HMMs), but relax certain assumptions about the input and output sequence distributions. An HMM can loosely be understood as a CRF with very specific feature functions that use constant probabilities to model state transitions and emissions. Conversely, a CRF can loosely be understood as a generalization of an HMM that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence. Notably, in contrast to HMMs, CRFs can contain any number of feature functions, the feature functions can inspect the entire input sequence X {\displaystyle X} at any point during inference, and the range of the feature functions need not have a probabilistic interpretation. == Variants == === Higher-order CRFs and semi-Markov CRFs === CRFs can be extended into higher order models by making each Y i {\displaystyle Y_{i}} dependent on a fixed number k {\displaystyle k} of previous variables Y i − k , . . . , Y i − 1 {\displaystyle Y_{i-k},...,Y_{i-1}} . In conventional formulations of higher order CRFs, training and inference are only practical for small values of k {\displaystyle k} (such as k ≤ 5), since their computational cost increases exponentially with k {\displaystyle k} . However, another recent advance has managed to ameliorate these issues by leveraging concepts and tools from the field of Bayesian nonparametrics. Specifically, the CRF-infinity approach constitutes a CRF-type model that is capable of learning infinitely-long temporal dynamics in a scalable fashion. This is effected by introducing a novel potential function for CRFs that is based on the Sequence Memoizer (SM), a nonparametric Bayesian model for learning infinitely-long dynamics in sequential observations. To render such a model computationally tractable, CRF-infinity employs a mean-field approximation of the postulated novel potential functions (which are driven by an SM). This allows for devising efficient approximate training and inference algorithms for the model, without undermining its capability to capture and model temporal dependencies of arbitrary length. There exists another generalization of CRFs, the semi-Markov conditional random field (semi-CRF), which models variable-length segmentations of the label sequence Y {\displaystyle Y} . This provides much of the power of higher-order CRFs to model long-range dependencies of the Y i {\displaystyle Y_{i}} , at a reasonable computational cost. Finally, large-margin models for structured prediction, such as the structured Support Vector Machine can be seen as an alternative training procedure to CRFs. === Latent-dynamic conditional random field === Latent-dynamic conditional random fields (LDCRF) or discriminative probabilistic latent variable models (DPLVM) are a type of CRFs for sequence tagging tasks. They are latent variable models that are trained discriminatively. In an LDCRF, like in any sequence tagging task, given a sequence of observations x = x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} , the main problem the model must solve is how to assign a sequence of labels y = y 1 , … , y n {\displaystyle y_{1},\dots ,y_{n}} from one finite set