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Section: Bias mitigation strategies > Inprocessing > Adversarial debiasing. We train two classifiers at the same time through some gradient-based method (f.e.: gradient descent). The first one, the predictor tries to accomplish the task of predicting Y {\textstyle Y} , the target variable, given X {\textstyle X} , the ... | Wikipedia - Fairness (machine learning) - Bias mitigation strategies > Inprocessing > Adversarial debiasing | 298 | 1,045 | null |
An important point here is that, to propagate correctly, Y ^ {\textstyle {\hat {Y}}} above must refer to the raw output of the classifier, not the discrete prediction; for example, with an artificial neural network and a classification problem, Y ^ {\textstyle {\hat {Y}}} could refer to the output of the softmax layer.... | Wikipedia - Fairness (machine learning) - Bias mitigation strategies > Inprocessing > Adversarial debiasing | 254 | 752 | null |
Then we update U {\textstyle U} to minimize L A {\textstyle L_{A}} at each training step according to the gradient ∇ U L A {\textstyle \nabla _{U}L_{A}} and we modify W {\textstyle W} according to the expression: ∇ W L P − p r o j ∇ W L A ∇ W L P − α ∇ W L A {\displaystyle \nabla _{W}L_{P}-proj_{\nabla _{W}L_{A}}\nabla... | Wikipedia - Fairness (machine learning) - Bias mitigation strategies > Inprocessing > Adversarial debiasing | 302 | 812 | null |
The intuitive idea is that we want the predictor to try to minimize L P {\textstyle L_{P}} (therefore the term ∇ W L P {\textstyle \nabla _{W}L_{P}} ) while, at the same time, maximize L A {\textstyle L_{A}} (therefore the term − α ∇ W L A {\textstyle -\alpha \nabla _{W}L_{A}} ), so that the adversary fails at predicti... | Wikipedia - Fairness (machine learning) - Bias mitigation strategies > Inprocessing > Adversarial debiasing | 225 | 734 | null |
Section: Bias mitigation strategies > Postprocessing. The final method tries to correct the results of a classifier to achieve fairness. In this method, we have a classifier that returns a score for each individual and we need to do a binary prediction for them. High scores are likely to get a positive outcome, while l... | Wikipedia - Fairness (machine learning) - Bias mitigation strategies > Postprocessing | 215 | 1,077 | null |
Section: Bias mitigation strategies > Postprocessing > Reject option based classification. Given a classifier let P ( + | X ) {\textstyle P(+|X)} be the probability computed by the classifiers as the probability that the instance X {\textstyle X} belongs to the positive class +. When P ( + | X ) {\textstyle P(+|X)} is ... | Wikipedia - Fairness (machine learning) - Bias mitigation strategies > Postprocessing > Reject option based classification | 319 | 1,069 | null |
Section: Feature types. In feature engineering, two types of features are commonly used: numerical and categorical. Numerical features are continuous values that can be measured on a scale. Examples of numerical features include age, height, weight, and income. Numerical features can be used in machine learning algorit... | Wikipedia - Feature (machine learning) - Feature types | 191 | 1,058 | null |
Section: Feature vectors. In pattern recognition and machine learning, a feature vector is an n-dimensional vector of numerical features that represent some object. Many algorithms in machine learning require a numerical representation of objects, since such representations facilitate processing and statistical analysi... | Wikipedia - Feature (machine learning) - Feature vectors | 257 | 1,459 | null |
Feature construction is the application of a set of constructive operators to a set of existing features resulting in construction of new features. Examples of such constructive operators include checking for the equality conditions {=, ≠}, the arithmetic operators {+,−,×, /}, the array operators {max(S), min(S), avera... | Wikipedia - Feature (machine learning) - Feature vectors | 156 | 820 | null |
Section: Clustering. One of the applications of feature engineering has been clustering of feature-objects or sample-objects in a dataset. Especially, feature engineering based on matrix decomposition has been extensively used for data clustering under non-negativity constraints on the feature coefficients. These inclu... | Wikipedia - Feature engineering - Clustering | 308 | 1,603 | null |
Section: Predictive modelling. Feature engineering in machine learning and statistical modeling involves selecting, creating, transforming, and extracting data features. Key components include feature creation from existing data, transforming and imputing missing or invalid features, reducing data dimensionality throug... | Wikipedia - Feature engineering - Predictive modelling | 207 | 1,221 | null |
Section: Automation > Open-source implementations. There are a number of open-source libraries and tools that automate feature engineering on relational data and time series: featuretools is a Python library for transforming time series and relational data into feature matrices for machine learning. MCMD: An open-sourc... | Wikipedia - Feature engineering - Automation > Open-source implementations | 348 | 1,659 | null |
Section: Feature stores. The feature store is where the features are stored and organized for the explicit purpose of being used to either train models (by data scientists) or make predictions (by applications that have a trained model). It is a central location where you can either create or update groups of features ... | Wikipedia - Feature engineering - Feature stores | 169 | 943 | null |
Article: Feature hashing. In machine learning, feature hashing, also known as the hashing trick (by analogy to the kernel trick), is a fast and space-efficient way of vectorizing features, i.e. turning arbitrary features into indices in a vector or matrix. It works by applying a hash function to the features and using ... | Wikipedia - Feature hashing - Summary | 155 | 716 | null |
Section: Motivation > Motivating example. In a typical document classification task, the input to the machine learning algorithm (both during learning and classification) is free text. From this, a bag of words (BOW) representation is constructed: the individual tokens are extracted and counted, and each distinct token... | Wikipedia - Feature hashing - Motivation > Motivating example | 275 | 1,350 | null |
Mary likes movies too. John also likes football. can be converted, using the dictionary to the term-document matrix ( John likes to watch movies Mary too also football 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 ) {\displaystyle {\begin{pmatrix}{\textrm {John}}&{\textrm {likes}}&{\textrm {to}}&{\textrm {watch... | Wikipedia - Feature hashing - Motivation > Motivating example | 337 | 1,043 | null |
Section: Motivation > Mathematical motivation. Mathematically, a token is an element t {\displaystyle t} in a finite (or countably infinite) set T {\displaystyle T} . Suppose we only need to process a finite corpus, then we can put all tokens appearing in the corpus into T {\displaystyle T} , meaning that T {\displayst... | Wikipedia - Feature hashing - Motivation > Mathematical motivation | 311 | 977 | null |
, t m } {\displaystyle T=\{t_{1},t_{2},..,t_{m}\}} , then define ϕ ( t i ) = e i {\displaystyle \phi (t_{i})=e_{i}} . In other words, we assign a unique index i {\displaystyle i} to each token, then map the token with index i {\displaystyle i} to the unit basis vector e i {\displaystyle e_{i}} . One-hot encoding is eas... | Wikipedia - Feature hashing - Motivation > Mathematical motivation | 330 | 931 | null |
. . , n } {\displaystyle h:T\to \{1,...,n\}} , then use ϕ ( t ) = e h ( t ) {\displaystyle \phi (t)=e_{h(t)}} . In practice, there is no simple way to construct an efficient injection h : T → { 1 , . . . , n } {\displaystyle h:T\to \{1,...,n\}} . However, we do not need a strict injection, but only an approximate injec... | Wikipedia - Feature hashing - Motivation > Mathematical motivation | 241 | 665 | null |
Section: Algorithms > Feature hashing (Weinberger et al. 2009). The basic feature hashing algorithm presented in (Weinberger et al. 2009) is defined as follows. First, one specifies two hash functions: the kernel hash h : T → { 1 , 2 , . . . , n } {\displaystyle h:T\to \{1,2,...,n\}} , and the sign hash ζ : T → { − 1 ,... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) | 344 | 881 | null |
, t k ) = ∑ j = 1 k ϕ ( t j ) {\displaystyle \phi :T^{*}\to \mathbb {R} ^{n},\quad \phi (t_{1},...,t_{k})=\sum _{j=1}^{k}\phi (t_{j})} where T ∗ {\displaystyle T^{*}} is the set of all finite strings consisting of tokens in T {\displaystyle T} . Equivalently, ϕ ( t 1 , . . . , t k ) = ∑ j = 1 k ζ ( t j ) e h ( t j ) = ... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) | 282 | 514 | null |
To make it nicer, we lift it to T → R T {\displaystyle T\to \mathbb {R} ^{T}} , and lift ϕ {\displaystyle \phi } from ϕ : T → R n {\displaystyle \phi :T\to \mathbb {R} ^{n}} to ϕ : R T → R n {\displaystyle \phi :\mathbb {R} ^{T}\to \mathbb {R} ^{n}} by linear extension: ϕ ( ( x t ) t ∈ T ) = ∑ t ∈ T x t ζ ( t ) e h ( t... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) > Geometric properties | 321 | 796 | null |
One may impose a metric, then take its completion, to allow well-behaved infinite sums, or one may demand that nothing is actually infinite, only potentially so. Here, we go for the potential-infinity way, by restricting R T {\displaystyle \mathbb {R} ^{T}} to contain only vectors with finite support: ∀ ( x t ) t ∈ T ∈... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) > Geometric properties | 203 | 608 | null |
Define an inner product on R T {\displaystyle \mathbb {R} ^{T}} in the obvious way: ⟨ e t , e t ′ ⟩ = { 1 , if t = t ′ , 0 , else. ⟨ x , x ′ ⟩ = ∑ t , t ′ ∈ T x t x t ′ ⟨ e t , e t ′ ⟩ {\displaystyle \langle e_{t},e_{t'}\rangle ={\begin{cases}1,{\text{ if }}t=t',\\0,{\text{ else.}}\end{cases}}\quad \langle x,x'\rangle ... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) > Geometric properties | 312 | 799 | null |
Now we have an inner product space, with enough structure to describe the geometry of the feature hashing function ϕ : R T → R n {\displaystyle \phi :\mathbb {R} ^{T}\to \mathbb {R} ^{n}} . First, we can see why h {\displaystyle h} is called a "kernel hash": it allows us to define a kernel K : T × T → R {\displaystyle ... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) > Geometric properties | 310 | 801 | null |
First, we can see why h {\displaystyle h} is called a "kernel hash": it allows us to define a kernel K : T × T → R {\displaystyle K:T\times T\to \mathbb {R} } by K ( t , t ′ ) = ⟨ e h ( t ) , e h ( t ′ ) ⟩ {\displaystyle K(t,t')=\langle e_{h(t)},e_{h(t')}\rangle } In the language of the "kernel trick", K {\displaystyle... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) > Geometric properties | 433 | 1,092 | null |
In fact, we have been using another kernel K ζ : T × T → R {\displaystyle K_{\zeta }:T\times T\to \mathbb {R} } , defined by K ζ ( t , t ′ ) = ⟨ ζ ( t ) e h ( t ) , ζ ( t ′ ) e h ( t ′ ) ⟩ {\displaystyle K_{\zeta }(t,t')=\langle \zeta (t)e_{h(t)},\zeta (t')e_{h(t')}\rangle } The benefit of augmenting the kernel hash h ... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) > Geometric properties | 358 | 930 | null |
The above statement and proof interprets the binary hash function ζ {\displaystyle \zeta } not as a deterministic function of type T → { − 1 , + 1 } {\displaystyle T\to \{-1,+1\}} , but as a random binary vector { − 1 , + 1 } T {\displaystyle \{-1,+1\}^{T}} with unbiased entries, meaning that P r ( ζ ( t ) = + 1 ) = P ... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) > Geometric properties | 195 | 544 | null |
Section: Algorithms > Feature hashing (Weinberger et al. 2009) > Pseudocode implementation. Instead of maintaining a dictionary, a feature vectorizer that uses the hashing trick can build a vector of a pre-defined length by applying a hash function h to the features (e.g., words), then using the hash values directly as... | Wikipedia - Feature hashing - Algorithms > Feature hashing (Weinberger et al. 2009) > Pseudocode implementation | 327 | 1,313 | null |
Section: Algorithms > Extensions and variations > Learned feature hashing. Feature hashing generally suffers from hash collision, which means that there exist pairs of different tokens with the same hash: t ≠ t ′ , ϕ ( t ) = ϕ ( t ′ ) = v {\displaystyle t\neq t',\phi (t)=\phi (t')=v} . A machine learning model trained ... | Wikipedia - Feature hashing - Algorithms > Extensions and variations > Learned feature hashing | 215 | 867 | null |
Section: Applications and practical performance. Ganchev and Dredze showed that in text classification applications with random hash functions and several tens of thousands of columns in the output vectors, feature hashing need not have an adverse effect on classification performance, even without the signed hash funct... | Wikipedia - Feature hashing - Applications and practical performance | 343 | 1,417 | null |
Article: Feature learning. In machine learning (ML), feature learning or representation learning is a set of techniques that allow a system to automatically discover the representations needed for feature detection or classification from raw data. This replaces manual feature engineering and allows a machine to both le... | Wikipedia - Feature learning - Summary | 349 | 1,909 | null |
Section: Supervised > Supervised dictionary learning. Dictionary learning develops a set (dictionary) of representative elements from the input data such that each data point can be represented as a weighted sum of the representative elements. The dictionary elements and the weights may be found by minimizing the avera... | Wikipedia - Feature learning - Supervised > Supervised dictionary learning | 224 | 1,227 | null |
Section: Supervised > Neural networks. Neural networks are a family of learning algorithms that use a "network" consisting of multiple layers of inter-connected nodes. It is inspired by the animal nervous system, where the nodes are viewed as neurons and edges are viewed as synapses. Each edge has an associated weight,... | Wikipedia - Feature learning - Supervised > Neural networks | 191 | 1,040 | null |
Section: Unsupervised > K-means clustering. K-means clustering is an approach for vector quantization. In particular, given a set of n vectors, k-means clustering groups them into k clusters (i.e., subsets) in such a way that each vector belongs to the cluster with the closest mean. The problem is computationally NP-ha... | Wikipedia - Feature learning - Unsupervised > K-means clustering | 333 | 1,529 | null |
Section: Unsupervised > Principal component analysis. Principal component analysis (PCA) is often used for dimension reduction. Given an unlabeled set of n input data vectors, PCA generates p (which is much smaller than the dimension of the input data) right singular vectors corresponding to the p largest singular valu... | Wikipedia - Feature learning - Unsupervised > Principal component analysis | 327 | 1,570 | null |
Section: Unsupervised > Local linear embedding. Local linear embedding (LLE) is a nonlinear learning approach for generating low-dimensional neighbor-preserving representations from (unlabeled) high-dimension input. The approach was proposed by Roweis and Saul (2000). The general idea of LLE is to reconstruct the origi... | Wikipedia - Feature learning - Unsupervised > Local linear embedding | 336 | 1,661 | null |
Section: Multilayer/deep architectures > Restricted Boltzmann machine. Restricted Boltzmann machines (RBMs) are often used as a building block for multilayer learning architectures. An RBM can be represented by an undirected bipartite graph consisting of a group of binary hidden variables, a group of visible variables,... | Wikipedia - Feature learning - Multilayer/deep architectures > Restricted Boltzmann machine | 333 | 1,695 | null |
Section: Multilayer/deep architectures > Autoencoder. An autoencoder consisting of an encoder and a decoder is a paradigm for deep learning architectures. An example is provided by Hinton and Salakhutdinov where the encoder uses raw data (e.g., image) as input and produces feature or representation as output and the de... | Wikipedia - Feature learning - Multilayer/deep architectures > Autoencoder | 193 | 902 | null |
Section: Self-supervised. Self-supervised representation learning is learning features by training on the structure of unlabeled data rather than relying on explicit labels for an information signal. This approach has enabled the combined use of deep neural network architectures and larger unlabeled datasets to produce... | Wikipedia - Feature learning - Self-supervised | 307 | 1,606 | null |
Section: Self-supervised > Text. Word2vec is a word embedding technique which learns to represent words through self-supervision over each word and its neighboring words in a sliding window across a large corpus of text. The model has two possible training schemes to produce word vector representations, one generative ... | Wikipedia - Feature learning - Self-supervised > Text | 261 | 1,351 | null |
Section: Self-supervised > Image. The domain of image representation learning has employed many different self-supervised training techniques, including transformation, inpainting, patch discrimination and clustering. Examples of generative approaches are Context Encoders, which trains an AlexNet CNN architecture to ge... | Wikipedia - Feature learning - Self-supervised > Image | 211 | 1,138 | null |
Section: Self-supervised > Graph. The goal of many graph representation learning techniques is to produce an embedded representation of each node based on the overall network topology. node2vec extends the word2vec training technique to nodes in a graph by using co-occurrence in random walks through the graph as the me... | Wikipedia - Feature learning - Self-supervised > Graph | 160 | 907 | null |
Section: Self-supervised > Multimodal. Self-supervised learning has also been used to develop joint representations of multiple data types. Approaches usually rely on some natural or human-derived association between the modalities as an implicit label, for instance video clips of animals or objects with characteristic... | Wikipedia - Feature learning - Self-supervised > Multimodal | 280 | 1,488 | null |
Section: Motivation. Since the range of values of raw data varies widely, in some machine learning algorithms, objective functions will not work properly without normalization. For example, many classifiers calculate the distance between two points by the Euclidean distance. If one of the features has a broad range of ... | Wikipedia - Feature scaling - Motivation | 219 | 1,214 | null |
Section: Methods > Rescaling (min-max normalization). Also known as min-max scaling or min-max normalization, rescaling is the simplest method and consists in rescaling the range of features to scale the range in [0, 1] or [−1, 1]. Selecting the target range depends on the nature of the data. The general formula for a ... | Wikipedia - Feature scaling - Methods > Rescaling (min-max normalization) | 253 | 843 | null |
To rescale this data, we first subtract 160 from each student's weight and divide the result by 40 (the difference between the maximum and minimum weights). To rescale a range between an arbitrary set of values [a, b], the formula becomes: x ′ = a + ( x − min ( x ) ) ( b − a ) max ( x ) − min ( x ) {\displaystyle x'=a+... | Wikipedia - Feature scaling - Methods > Rescaling (min-max normalization) | 163 | 444 | null |
Section: Methods > Mean normalization. x ′ = x − x ¯ max ( x ) − min ( x ) {\displaystyle x'={\frac {x-{\bar {x}}}{{\text{max}}(x)-{\text{min}}(x)}}} where x {\displaystyle x} is an original value, x ′ {\displaystyle x'} is the normalized value, x ¯ = average ( x ) {\displaystyle {\bar {x}}={\text{average}}(x)} is the ... | Wikipedia - Feature scaling - Methods > Mean normalization | 158 | 475 | null |
Section: Methods > Standardization (Z-score Normalization). In machine learning, we can handle various types of data, e.g. audio signals and pixel values for image data, and this data can include multiple dimensions. Feature standardization makes the values of each feature in the data have zero-mean (when subtracting t... | Wikipedia - Feature scaling - Methods > Standardization (Z-score Normalization) | 263 | 1,072 | null |
Section: Methods > Robust Scaling. Robust scaling, also known as standardization using median and interquartile range (IQR), is designed to be robust to outliers. It scales features using the median and IQR as reference points instead of the mean and standard deviation: x ′ = x − Q 2 ( x ) Q 3 ( x ) − Q 1 ( x ) {\displ... | Wikipedia - Feature scaling - Methods > Robust Scaling | 191 | 524 | null |
For example, if x = ( v 1 , v 2 , v 3 ) {\displaystyle x=(v_{1},v_{2},v_{3})} , then its Lp-normalized version is: ( v 1 ( | v 1 | p + | v 2 | p + | v 3 | p ) 1 / p , v 2 ( | v 1 | p + | v 2 | p + | v 3 | p ) 1 / p , v 3 ( | v 1 | p + | v 2 | p + | v 3 | p ) 1 / p ) {\displaystyle \left({\frac {v_{1}}{(|v_{1}|^{p}+|v_{... | Wikipedia - Feature scaling - Methods > Unit vector normalization | 312 | 478 | null |
Article: Feature store. A feature store is a centralised repository or data storage layer where users can store, share, and discover curated features for machine learning (ML) models.The concept often associated with feature engineering facilitates the processing and transformation of raw data into consumable features ... | Wikipedia - Feature store - Summary | 219 | 1,250 | null |
Section: Deployment and availability. Feature stores can be built in-house by engineering teams or obtained from companies offering Feature Store solutions as Platform-as-a-Service (PaaS). These solutions can be cloud-based (online) or offered as on-premises (offline) deployments. The first feature stores, Michelangelo... | Wikipedia - Feature store - Deployment and availability | 157 | 709 | null |
Section: Functionality and advantages. Feature stores provide API-based access to structured and unstructured data for machine learning workloads, supporting efficient querying and retrieval. A significant advantage of feature stores is their ability to accelerate Machine learning model development and deployment. Engi... | Wikipedia - Feature store - Functionality and advantages | 193 | 1,115 | null |
Section: Key components of feature stores. The centralised feature management organises features and ensures that they are consistent, making them easily accessible to different teams and models. Features are consistent and can be reused different models, thus improving the reproducibility of ML projects. Real time and... | Wikipedia - Feature store - Key components of feature stores | 180 | 1,048 | null |
Section: Definition. Federated learning aims at training a machine learning algorithm, for instance deep neural networks, on multiple local datasets contained in local nodes without explicitly exchanging data samples. The general principle consists in training local models on local data samples and exchanging parameter... | Wikipedia - Federated learning - Definition | 302 | 1,581 | null |
Section: Definition > Mathematical formulation. The objective function for federated learning is as follows: f ( x 1 , … , x K ) = 1 K ∑ i = 1 K f i ( x i ) {\displaystyle f(\mathbf {x} _{1},\dots ,\mathbf {x} _{K})={\dfrac {1}{K}}\sum _{i=1}^{K}f_{i}(\mathbf {x} _{i})} where K {\displaystyle K} is the number of nodes,... | Wikipedia - Federated learning - Definition > Mathematical formulation | 328 | 924 | null |
Section: Main features > Iterative learning. To ensure good task performance of a final, central machine learning model, federated learning relies on an iterative process broken up into an atomic set of client-server interactions known as a federated learning round. Each round of this process consists in transmitting t... | Wikipedia - Federated learning - Main features > Iterative learning | 339 | 1,767 | null |
Reporting: each selected node sends its local model to the server for aggregation. The central server aggregates the received models and sends back the model updates to the nodes. It also handles failures for disconnected nodes or lost model updates. The next federated round is started returning to the client selection... | Wikipedia - Federated learning - Main features > Iterative learning | 235 | 1,290 | null |
Section: Main features > Non-IID data. In most cases, the assumption of independent and identically distributed samples across local nodes does not hold for federated learning setups. Under this setting, the performances of the training process may vary significantly according to the unbalanced local data samples as we... | Wikipedia - Federated learning - Main features > Non-IID data | 333 | 1,771 | null |
Section: Algorithmic hyper-parameters > Federated learning parameters. Once the topology of the node network is chosen, one can control different parameters of the federated learning process (in addition to the machine learning model's own hyperparameters) to optimize learning: Number of federated learning rounds: T {\... | Wikipedia - Federated learning - Algorithmic hyper-parameters > Federated learning parameters | 251 | 1,134 | null |
Section: Technical limitations. Federated learning requires frequent communication between nodes during the learning process. Thus, it requires not only enough local computing power and memory, but also high bandwidth connections to be able to exchange parameters of the machine learning model. However, the technology a... | Wikipedia - Federated learning - Technical limitations | 306 | 1,612 | null |
Section: Variations > Federated learning with dynamic regularization (FedDyn). Federated learning methods suffer when node datasets are distributed heterogeneously, because then minimizing the node losses is not the same as minimizing the global loss. In 2021, Acar et al. introduced a solution called FedDyn, which dyna... | Wikipedia - Federated learning - Variations > Federated learning with dynamic regularization (FedDyn) | 275 | 1,261 | null |
Section: Variations > Personalized federated learning by pruning (Sub-FedAvg). Federated learning methods have poor global performance under non-IID settings. This motivates clients to yield personalized models in federation. To change this, Vahidian et al. recently introduced the algorithm Sub-FedAvg which does hybrid... | Wikipedia - Federated learning - Variations > Personalized federated learning by pruning (Sub-FedAvg) | 201 | 977 | null |
Section: Variations > Hybrid federated dual coordinate ascent (HyFDCA). Very few methods for hybrid federated learning, where clients only hold subsets of both features and samples, exist. Yet, this scenario is very important in practical settings. Hybrid Federated Dual Coordinate Ascent (HyFDCA) is a novel algorithm p... | Wikipedia - Federated learning - Variations > Hybrid federated dual coordinate ascent (HyFDCA) | 313 | 1,430 | null |
These principles apply to future efforts in developing primal-dual algorithms for FL. HyFDCA empirically outperforms HyFEM and FedAvg in loss function value and validation accuracy across a multitude of problem settings and datasets (see below for more details). The authors also introduce a hyperparameter selection fra... | Wikipedia - Federated learning - Variations > Hybrid federated dual coordinate ascent (HyFDCA) | 344 | 1,697 | null |
HyFDCA is empirically benchmarked against the aforementioned HyFEM as well as the popular FedAvg in solving convex problem (specifically classification problems) for several popular datasets (MNIST, Covtype, and News20). The authors found HyFDCA converges to a lower loss value and higher validation accuracy in less ove... | Wikipedia - Federated learning - Variations > Hybrid federated dual coordinate ascent (HyFDCA) | 198 | 866 | null |
Section: Current research topics. Federated learning has started to emerge as an important research topic in 2015 and 2016, with the first publications on federated averaging in telecommunication settings. Before that, in a thesis work titled "A Framework for Multi-source Prefetching Through Adaptive Weight", an approa... | Wikipedia - Federated learning - Current research topics | 314 | 1,860 | null |
Section: Use cases > Medicine: digital health. Federated learning seeks to address the problem of data governance and privacy by training algorithms collaboratively without exchanging the data itself. Today's standard approach of centralizing data from multiple centers comes at the cost of critical concerns regarding p... | Wikipedia - Federated learning - Use cases > Medicine: digital health | 333 | 1,883 | null |
Section: Use cases > Robotics. Robotics includes a wide range of applications of machine learning methods: from perception and decision-making to control. As robotic technologies have been increasingly deployed from simple and repetitive tasks (e.g. repetitive manipulation) to complex and unpredictable tasks (e.g. auto... | Wikipedia - Federated learning - Use cases > Robotics | 167 | 915 | null |
Section: Use cases > Biometrics. Federated Learning (FL) is transforming biometric recognition by enabling collaborative model training across distributed data sources while preserving privacy. By eliminating the need to share sensitive biometric templates like fingerprints, facial images, and iris scans, FL addresses ... | Wikipedia - Federated learning - Use cases > Biometrics | 175 | 1,038 | null |
Article: Fine-tuning (deep learning). In deep learning, fine-tuning is an approach to transfer learning in which the parameters of a pre-trained neural network model are trained on new data. Fine-tuning can be done on the entire neural network, or on only a subset of its layers, in which case the layers that are not be... | Wikipedia - Fine-tuning (deep learning) - Summary | 334 | 1,556 | null |
Section: Variants > Low-rank adaptation. Low-rank adaptation (LoRA) is an adapter-based technique for efficiently fine-tuning models. The basic idea is to design a low-rank matrix that is then added to the original matrix. An adapter, in this context, is a collection of low-rank matrices which, when added to a base mod... | Wikipedia - Fine-tuning (deep learning) - Variants > Low-rank adaptation | 186 | 875 | null |
Section: Variants > Representation fine-tuning. Representation fine-tuning (ReFT) is a technique developed by researchers at Stanford University aimed at fine-tuning large language models (LLMs) by modifying less than 1% of their representations. Unlike parameter-efficient fine-tuning (PEFT) methods, which mainly focus... | Wikipedia - Fine-tuning (deep learning) - Variants > Representation fine-tuning | 193 | 1,020 | null |
Article: Flow-based generative model. A flow-based generative model is a generative model used in machine learning that explicitly models a probability distribution by leveraging normalizing flow, which is a statistical method using the change-of-variable law of probabilities to transform a simple distribution into a c... | Wikipedia - Flow-based generative model - Summary | 151 | 803 | null |
Section: Method. Let z 0 {\displaystyle z_{0}} be a (possibly multivariate) random variable with distribution p 0 ( z 0 ) {\displaystyle p_{0}(z_{0})} . For i = 1 , . . . , K {\displaystyle i=1,...,K} , let z i = f i ( z i − 1 ) {\displaystyle z_{i}=f_{i}(z_{i-1})} be a sequence of random variables transformed from z 0... | Wikipedia - Flow-based generative model - Method | 221 | 574 | null |
The final output z K {\displaystyle z_{K}} models the target distribution. The log likelihood of z K {\displaystyle z_{K}} is (see derivation): log p K ( z K ) = log p 0 ( z 0 ) − ∑ i = 1 K log | det d f i ( z i − 1 ) d z i − 1 | {\displaystyle \log p_{K}(z_{K})=\log p_{0}(z_{0})-\sum _{i=1}^{K}\log \left|\det {\... | Wikipedia - Flow-based generative model - Method | 336 | 1,019 | null |
Section: Method > Derivation of log likelihood. Consider z 1 {\displaystyle z_{1}} and z 0 {\displaystyle z_{0}} . Note that z 0 = f 1 − 1 ( z 1 ) {\displaystyle z_{0}=f_{1}^{-1}(z_{1})} . By the change of variable formula, the distribution of z 1 {\displaystyle z_{1}} is: p 1 ( z 1 ) = p 0 ( z 0 ) | det d f 1 − 1 ( z ... | Wikipedia - Flow-based generative model - Method > Derivation of log likelihood | 286 | 601 | null |
By the inverse function theorem: p 1 ( z 1 ) = p 0 ( z 0 ) | det ( d f 1 ( z 0 ) d z 0 ) − 1 | {\displaystyle p_{1}(z_{1})=p_{0}(z_{0})\left|\det \left({\frac {df_{1}(z_{0})}{dz_{0}}}\right)^{-1}\right|} By the identity det ( A − 1 ) = det ( A ) − 1 {\displaystyle \det(A^{-1})=\det(A)^{-1}} (where A {\displaystyle A} i... | Wikipedia - Flow-based generative model - Method > Derivation of log likelihood | 346 | 665 | null |
\left|\det {\frac {df_{1}(z_{0})}{dz_{0}}}\right|} In general, the above applies to any z i {\displaystyle z_{i}} and z i − 1 {\displaystyle z_{i-1}} . Since log p i ( z i ) {\displaystyle \log p_{i}(z_{i})} is equal to log p i − 1 ( z i − 1 ) {\displaystyle \log p_{i-1}(z_{i-1})} subtracted by a non-recursive term... | Wikipedia - Flow-based generative model - Method > Derivation of log likelihood | 286 | 571 | null |
Section: Training method. As is generally done when training a deep learning model, the goal with normalizing flows is to minimize the Kullback–Leibler divergence between the model's likelihood and the target distribution to be estimated. Denoting p θ {\displaystyle p_{\theta }} the model's likelihood and p ∗ {\display... | Wikipedia - Flow-based generative model - Training method | 330 | 1,065 | null |
Indeed, if we have a dataset { x i } i = 1 N {\displaystyle \{x_{i}\}_{i=1}^{N}} of samples each independently drawn from the target distribution p ∗ ( x ) {\displaystyle p^{*}(x)} , then this term can be estimated as: − E ^ p ∗ ( x ) [ log p θ ( x ) ] = − 1 N ∑ i = 0 N log p θ ( x i ) {\displaystyle -{\hat {\matho... | Wikipedia - Flow-based generative model - Training method | 348 | 763 | null |
}(x_{i})} In other words, minimizing the Kullback–Leibler divergence between the model's likelihood and the target distribution is equivalent to maximizing the model likelihood under observed samples of the target distribution. A pseudocode for training normalizing flows is as follows: INPUT. dataset x 1 : n {\displays... | Wikipedia - Flow-based generative model - Training method | 187 | 580 | null |
Section: Variants > Planar Flow. The earliest example. Fix some activation function h {\displaystyle h} , and let θ = ( u , w , b ) {\displaystyle \theta =(u,w,b)} with the appropriate dimensions, then x = f θ ( z ) = z + u h ( ⟨ w , z ⟩ + b ) {\displaystyle x=f_{\theta }(z)=z+uh(\langle w,z\rangle +b)} The inverse f θ... | Wikipedia - Flow-based generative model - Variants > Planar Flow | 317 | 808 | null |
Section: Variants > Nonlinear Independent Components Estimation (NICE). Let x , z ∈ R 2 n {\displaystyle x,z\in \mathbb {R} ^{2n}} be even-dimensional, and split them in the middle. Then the normalizing flow functions are x = [ x 1 x 2 ] = f θ ( z ) = [ z 1 z 2 ] + [ 0 m θ ( z 1 ) ] {\displaystyle x={\begin{bmatrix}x_{... | Wikipedia - Flow-based generative model - Variants > Nonlinear Independent Components Estimation (NICE) | 328 | 769 | null |
Section: Variants > Real Non-Volume Preserving (Real NVP). The Real Non-Volume Preserving model generalizes NICE model by: x = [ x 1 x 2 ] = f θ ( z ) = [ z 1 e s θ ( z 1 ) ⊙ z 2 ] + [ 0 m θ ( z 1 ) ] {\displaystyle x={\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}=f_{\theta }(z)={\begin{bmatrix}z_{1}\\e^{s_{\theta }(z_{1})... | Wikipedia - Flow-based generative model - Variants > Real Non-Volume Preserving (Real NVP) | 348 | 668 | null |
The Real Non-Volume Preserving model generalizes NICE model by: x = [ x 1 x 2 ] = f θ ( z ) = [ z 1 e s θ ( z 1 ) ⊙ z 2 ] + [ 0 m θ ( z 1 ) ] {\displaystyle x={\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}=f_{\theta }(z)={\begin{bmatrix}z_{1}\\e^{s_{\theta }(z_{1})}\odot z_{2}\end{bmatrix}}+{\begin{bmatrix}0\\m_{\theta }(z... | Wikipedia - Flow-based generative model - Variants > Real Non-Volume Preserving (Real NVP) | 357 | 688 | null |
Section: Variants > Generative Flow (Glow). In generative flow model, each layer has 3 parts: channel-wise affine transform y c i j = s c ( x c i j + b c ) {\displaystyle y_{cij}=s_{c}(x_{cij}+b_{c})} with Jacobian ∏ c s c H W {\displaystyle \prod _{c}s_{c}^{HW}} . invertible 1x1 convolution z c i j = ∑ c ′ K c c ′ y c... | Wikipedia - Flow-based generative model - Variants > Generative Flow (Glow) | 264 | 690 | null |
An autoregressive model of a distribution on R n {\displaystyle \mathbb {R} ^{n}} is defined as the following stochastic process: x 1 ∼ N ( μ 1 , σ 1 2 ) x 2 ∼ N ( μ 2 ( x 1 ) , σ 2 ( x 1 ) 2 ) ⋯ x n ∼ N ( μ n ( x 1 : n − 1 ) , σ n ( x 1 : n − 1 ) 2 ) {\displaystyle {\begin{aligned}x_{1}\sim &N(\mu _{1},\sigma _{1}^{2}... | Wikipedia - Flow-based generative model - Variants > Masked Autoregressive Flow (MAF) | 349 | 691 | null |
model. By the reparameterization trick, the autoregressive model is generalized to a normalizing flow: x 1 = μ 1 + σ 1 z 1 x 2 = μ 2 ( x 1 ) + σ 2 ( x 1 ) z 2 ⋯ x n = μ n ( x 1 : n − 1 ) + σ n ( x 1 : n − 1 ) z n {\displaystyle {\begin{aligned}x_{1}=&\mu _{1}+\sigma _{1}z_{1}\\x_{2}=&\mu _{2}(x_{1})+\sigma _{2}(x_{1})z... | Wikipedia - Flow-based generative model - Variants > Masked Autoregressive Flow (MAF) | 286 | 622 | null |
The forward mapping is slow (because it's sequential), but the backward mapping is fast (because it's parallel). The Jacobian matrix is lower-diagonal, so the Jacobian is σ 1 σ 2 ( x 1 ) ⋯ σ n ( x 1 : n − 1 ) {\displaystyle \sigma _{1}\sigma _{2}(x_{1})\cdots \sigma _{n}(x_{1:n-1})} . Reversing the two maps f θ {\displ... | Wikipedia - Flow-based generative model - Variants > Masked Autoregressive Flow (MAF) | 172 | 496 | null |
Section: Variants > Continuous Normalizing Flow (CNF). Instead of constructing flow by function composition, another approach is to formulate the flow as a continuous-time dynamic. Let z 0 {\displaystyle z_{0}} be the latent variable with distribution p ( z 0 ) {\displaystyle p(z_{0})} . Map this latent variable to dat... | Wikipedia - Flow-based generative model - Variants > Continuous Normalizing Flow (CNF) | 188 | 575 | null |
neural networks. The inverse function is then naturally: z 0 = F − 1 ( x ) = z T + ∫ T 0 f ( z t , t ) d t = z T − ∫ 0 T f ( z t , t ) d t {\displaystyle z_{0}=F^{-1}(x)=z_{T}+\int _{T}^{0}f(z_{t},t)dt=z_{T}-\int _{0}^{T}f(z_{t},t)dt} And the log-likelihood of x {\displaystyle x} can be found as: log ( p ( x ) ) = lo... | Wikipedia - Flow-based generative model - Variants > Continuous Normalizing Flow (CNF) | 348 | 898 | null |
It is contrasted with previous discrete models of normalizing flow, where the Jacobian is carefully designed to be only upper- or lower-diagonal, so that the Jacobian can be evaluated efficiently. The trace can be estimated by "Hutchinson's trick":Given any matrix W ∈ R n × n {\displaystyle W\in \mathbb {R} ^{n\times n... | Wikipedia - Flow-based generative model - Variants > Continuous Normalizing Flow (CNF) | 286 | 903 | null |
Indeed, CNF was first proposed in the same paper that proposed neural ODE. There are two main deficiencies of CNF, one is that a continuous flow must be a homeomorphism, thus preserve orientation and ambient isotopy (for example, it's impossible to flip a left-hand to a right-hand by continuous deforming of space, and ... | Wikipedia - Flow-based generative model - Variants > Continuous Normalizing Flow (CNF) | 307 | 1,205 | null |
To regularize the flow f {\displaystyle f} , one can impose regularization losses. The paper proposed the following regularization loss based on optimal transport theory: λ K ∫ 0 T ‖ f ( z t , t ) ‖ 2 d t + λ J ∫ 0 T ‖ ∇ z f ( z t , t ) ‖ F 2 d t {\displaystyle \lambda _{K}\int _{0}^{T}\left\|f(z_{t},t)\right\|^{2}dt+\... | Wikipedia - Flow-based generative model - Variants > Continuous Normalizing Flow (CNF) | 261 | 725 | null |
Section: Downsides. Despite normalizing flows success in estimating high-dimensional densities, some downsides still exist in their designs. First of all, their latent space where input data is projected onto is not a lower-dimensional space and therefore, flow-based models do not allow for compression of data by defau... | Wikipedia - Flow-based generative model - Downsides | 280 | 1,378 | null |
Article: Flux (machine-learning framework). Flux is an open-source machine-learning software library and ecosystem written in Julia. Its current stable release is v0.15.0 . It has a layer-stacking-based interface for simpler models, and has a strong support on interoperability with other Julia packages instead of a mon... | Wikipedia - Flux (machine-learning framework) - Summary | 330 | 1,449 | null |
Article: Force control. Force control is the control of the force with which a machine or the manipulator of a robot acts on an object or its environment. By controlling the contact force, damage to the machine as well as to the objects to be processed and injuries when handling people can be prevented. In manufacturin... | Wikipedia - Force control - Summary | 315 | 1,687 | null |
Section: General. Controlling the contact force between a manipulator and its environment is an increasingly important task in the environment of mechanical manufacturing, as well as industrial and service robot. One motivation for the use of force control is safety for man and machine. For various reasons, movements o... | Wikipedia - Force control - General | 339 | 1,757 | null |
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