differance-engine / formalisms.yaml
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formalisms:
- id: pca
name: Principal Component Analysis
year: 1901
origin: Pearson; Hotelling (1933)
signature:
operation: project
domain: vector
codomain: vector
objective_family: none
meso_type: linear_projection
macro_type: eigenvalue_problem
canonical_reference: Pearson, K. (1901). On lines and planes of closest fit.
status: seed
- id: cca
name: Canonical Correlation Analysis
year: 1936
origin: Hotelling
signature:
operation: project
domain: vector
codomain: vector
objective_family: correlation
meso_type: joint_embedding
macro_type: eigenvalue_problem
canonical_reference: Hotelling, H. (1936). Relations between two sets of variates.
status: seed
- id: kernel_cca
name: Kernel Canonical Correlation Analysis
year: 2002
origin: Bach & Jordan
signature:
operation: project
domain: vector
codomain: vector
objective_family: correlation
meso_type: kernel_method
macro_type: eigenvalue_problem
canonical_reference: Bach, F.R. & Jordan, M.I. (2002). Kernel independent component analysis. JMLR.
status: seed
- id: ica
name: Independent Component Analysis
year: 1994
origin: Comon
signature:
operation: decompose
domain: vector
codomain: vector
objective_family: information
meso_type: linear_projection
macro_type: optimization
canonical_reference: Comon, P. (1994). Independent component analysis, a new concept?
status: seed
- id: fisher_lda
name: Fisher Linear Discriminant Analysis
year: 1936
origin: Fisher
signature:
operation: project
domain: vector
codomain: vector
objective_family: none
meso_type: linear_projection
macro_type: eigenvalue_problem
canonical_reference: Fisher, R.A. (1936). The use of multiple measurements in taxonomic problems.
status: seed
- id: mds
name: Multi-Dimensional Scaling
year: 1952
origin: Torgerson
signature:
operation: project
domain: matrix
codomain: vector
objective_family: none
meso_type: spectral_method
macro_type: eigenvalue_problem
canonical_reference: 'Torgerson, W.S. (1952). Multidimensional scaling: I. Theory and method.'
status: seed
- id: isomap
name: Isometric Feature Mapping
year: 2000
origin: Tenenbaum, de Silva & Langford
signature:
operation: project
domain: manifold
codomain: vector
objective_family: none
meso_type: spectral_method
macro_type: eigenvalue_problem
canonical_reference: Tenenbaum, J.B., de Silva, V., & Langford, J.C. (2000). A global geometric framework for nonlinear
dimensionality reduction. Science.
status: seed
- id: lle
name: Locally Linear Embedding
year: 2000
origin: Roweis & Saul
signature:
operation: project
domain: manifold
codomain: vector
objective_family: none
meso_type: spectral_method
macro_type: eigenvalue_problem
canonical_reference: Roweis, S.T. & Saul, L.K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science.
status: seed
- id: laplacian_eigenmaps
name: Laplacian Eigenmaps
year: 2003
origin: Belkin & Niyogi
signature:
operation: project
domain: manifold
codomain: vector
objective_family: energy
meso_type: spectral_method
macro_type: eigenvalue_problem
canonical_reference: Belkin, M. & Niyogi, P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation.
Neural Computation.
researchor_artifact_id: laplacian_matrix
status: seed
- id: svd
name: Singular Value Decomposition
year: 1873
origin: Beltrami; Jordan; Golub & Reinsch
signature:
operation: decompose
domain: matrix
codomain: matrix
objective_family: none
meso_type: linear_projection
macro_type: eigenvalue_problem
canonical_reference: Golub, G.H. & Reinsch, C. (1970). Singular value decomposition and least squares solutions.
researchor_artifact_id: singular_value_decomposition
status: seed
- id: nmf
name: Non-negative Matrix Factorization
year: 1999
origin: Lee & Seung
signature:
operation: decompose
domain: matrix
codomain: matrix
objective_family: divergence
meso_type: linear_projection
macro_type: optimization
canonical_reference: Lee, D.D. & Seung, H.S. (1999). Learning the parts of objects by non-negative matrix factorization.
Nature.
status: seed
canonical_arxiv_id: 0408058
- id: kernel_pca
name: Kernel Principal Component Analysis
year: 1998
origin: Schölkopf, Smola & Müller
signature:
operation: project
domain: vector
codomain: vector
objective_family: none
meso_type: kernel_method
macro_type: eigenvalue_problem
canonical_reference: Schölkopf, B., Smola, A., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue
problem. Neural Computation.
status: seed
- id: kernel_ridge_regression
name: Kernel Ridge Regression
year: 1998
origin: Saunders, Gammerman & Vovk; extended by many
signature:
operation: transform
domain: vector
codomain: scalar
objective_family: none
meso_type: kernel_method
macro_type: optimization
canonical_reference: Saunders, C., Gammerman, A., & Vovk, V. (1998). Ridge regression learning algorithm in dual variables.
ICML.
status: seed
- id: gaussian_process
name: Gaussian Process Regression
year: 1996
origin: Williams & Rasmussen; roots in kriging (Matheron 1963)
signature:
operation: transform
domain: vector
codomain: distribution
objective_family: likelihood
meso_type: kernel_method
macro_type: statistical_inference
canonical_reference: Rasmussen, C.E. & Williams, C.K.I. (2006). Gaussian Processes for Machine Learning. MIT Press.
status: seed
- id: svm
name: Support Vector Machine
year: 1995
origin: Cortes & Vapnik
signature:
operation: transform
domain: vector
codomain: assignment
objective_family: none
meso_type: kernel_method
macro_type: optimization
canonical_reference: Cortes, C. & Vapnik, V. (1995). Support-vector networks. Machine Learning.
status: seed
- id: mmd
name: Maximum Mean Discrepancy
year: 2006
origin: Gretton, Borgwardt, Rasch, Schölkopf & Smola
signature:
operation: match
domain: distribution
codomain: scalar
objective_family: none
meso_type: kernel_method
macro_type: statistical_inference
canonical_reference: Gretton, A. et al. (2012). A kernel two-sample test. JMLR.
status: seed
- id: kl_divergence_min
name: KL Divergence Minimization
year: 1951
origin: Kullback & Leibler
signature:
operation: minimize
domain: distribution
codomain: distribution
objective_family: divergence
meso_type: information_geometry
macro_type: optimization
canonical_reference: Kullback, S. & Leibler, R.A. (1951). On information and sufficiency.
researchor_artifact_id: relative_entropy
status: seed
- id: mutual_info_max
name: Mutual Information Maximization
year: 1948
origin: Shannon; McGill (1954)
signature:
operation: maximize
domain: distribution
codomain: scalar
objective_family: information
meso_type: information_geometry
macro_type: optimization
canonical_reference: Shannon, C.E. (1948). A mathematical theory of communication.
researchor_artifact_id: mutual_information
status: seed
- id: cross_entropy_min
name: Cross-Entropy Minimization
year: 1948
origin: Shannon; Good (1956)
signature:
operation: minimize
domain: distribution
codomain: distribution
objective_family: divergence
meso_type: information_geometry
macro_type: optimization
canonical_reference: Good, I.J. (1956). The population frequencies of species and the estimation of population parameters.
researchor_artifact_id: entropy
status: seed
- id: infonce
name: InfoNCE / Contrastive Estimation
year: 2018
origin: van den Oord, Li & Vinyals
signature:
operation: maximize
domain: vector
codomain: scalar
objective_family: information
meso_type: joint_embedding
macro_type: optimization
canonical_reference: van den Oord, A., Li, Y., & Vinyals, O. (2018). Representation learning with contrastive predictive
coding. arXiv:1807.03748.
status: seed
canonical_arxiv_id: '1807.03748'
- id: js_divergence
name: Jensen-Shannon Divergence
year: 1991
origin: Lin; extended from KL
signature:
operation: match
domain: distribution
codomain: scalar
objective_family: divergence
meso_type: information_geometry
macro_type: statistical_inference
canonical_reference: Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE Trans. Info. Theory.
status: seed
- id: elbo
name: Evidence Lower BOund Maximization
year: 1999
origin: Jordan, Ghahramani, Jaakkola & Saul; variational Bayes
signature:
operation: maximize
domain: distribution
codomain: distribution
objective_family: divergence
meso_type: variational
macro_type: optimization
canonical_reference: Jordan, M.I. et al. (1999). An introduction to variational methods for graphical models. Machine Learning.
status: seed
canonical_arxiv_id: '1312.6114'
- id: variational_inference
name: Variational Inference
year: 1990
origin: Hinton & van Camp; Jordan et al.; Wainwright & Jordan
signature:
operation: minimize
domain: distribution
codomain: distribution
objective_family: divergence
meso_type: variational
macro_type: statistical_inference
canonical_reference: Wainwright, M.J. & Jordan, M.I. (2008). Graphical models, exponential families, and variational inference.
Foundations & Trends in ML.
status: seed
- id: mean_field
name: Mean-Field Approximation
year: 1937
origin: Landau; Weiss; applied to stat mech and later VI
signature:
operation: minimize
domain: distribution
codomain: distribution
objective_family: divergence
meso_type: mean_field
macro_type: statistical_inference
canonical_reference: Parisi, G. (1988). Statistical Field Theory. Addison-Wesley.
status: seed
- id: mle
name: Maximum Likelihood Estimation
year: 1922
origin: Fisher
signature:
operation: maximize
domain: distribution
codomain: scalar
objective_family: likelihood
meso_type: probabilistic_inference
macro_type: statistical_inference
canonical_reference: Fisher, R.A. (1922). On the mathematical foundations of theoretical statistics.
status: seed
- id: map_estimation
name: Maximum A Posteriori Estimation
year: 1763
origin: Bayes; Laplace
signature:
operation: maximize
domain: distribution
codomain: scalar
objective_family: likelihood
meso_type: probabilistic_inference
macro_type: statistical_inference
canonical_reference: Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer.
status: seed
- id: em_algorithm
name: Expectation-Maximization
year: 1977
origin: Dempster, Laird & Rubin
signature:
operation: maximize
domain: distribution
codomain: distribution
objective_family: likelihood
meso_type: variational
macro_type: optimization
canonical_reference: Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the
EM algorithm. JRSS-B.
status: seed
- id: mcmc
name: Markov Chain Monte Carlo
year: 1953
origin: Metropolis, Rosenbluth, Rosenbluth, Teller & Teller; Hastings (1970)
signature:
operation: sample
domain: distribution
codomain: sequence
objective_family: none
meso_type: probabilistic_inference
macro_type: stochastic_process
canonical_reference: Metropolis, N. et al. (1953). Equation of state calculations by fast computing machines.
researchor_artifact_id: markov_chain
status: seed
- id: empirical_bayes
name: Empirical Bayes / Type-II Maximum Likelihood
year: 1955
origin: Robbins; Efron & Morris
signature:
operation: maximize
domain: distribution
codomain: distribution
objective_family: likelihood
meso_type: probabilistic_inference
macro_type: statistical_inference
canonical_reference: Robbins, H. (1955). An empirical Bayes approach to statistics. Proc. Third Berkeley Symp.
status: seed
- id: normalizing_flow
name: Normalizing Flow
year: 2015
origin: Rezende & Mohamed; Dinh, Krueger & Bengio (NICE 2014)
signature:
operation: transform
domain: distribution
codomain: distribution
objective_family: likelihood
meso_type: variational
macro_type: statistical_inference
canonical_reference: Rezende, D.J. & Mohamed, S. (2015). Variational inference with normalizing flows. ICML.
status: seed
canonical_arxiv_id: '1505.05770'
- id: boltzmann_distribution
name: Boltzmann / Gibbs Distribution
year: 1868
origin: Boltzmann; Gibbs (1902)
signature:
operation: sample
domain: scalar_field
codomain: distribution
objective_family: energy
meso_type: energy_model
macro_type: hamiltonian_system
canonical_reference: Gibbs, J.W. (1902). Elementary Principles in Statistical Mechanics.
researchor_mental_model_id: ergodicity
status: seed
- id: free_energy_min
name: Free Energy Minimization
year: 1873
origin: Helmholtz; Gibbs
signature:
operation: minimize
domain: distribution
codomain: distribution
objective_family: energy
meso_type: energy_model
macro_type: hamiltonian_system
canonical_reference: Helmholtz, H. (1882). Die Thermodynamik chemischer Vorgänge.
researchor_mental_model_id: phase_transitions
status: seed
- id: hopfield_network
name: Hopfield Network / Spin Glass
year: 1982
origin: Hopfield; Sherrington & Kirkpatrick (1975 spin glass)
signature:
operation: minimize
domain: vector
codomain: assignment
objective_family: energy
meso_type: spin_system
macro_type: hamiltonian_system
canonical_reference: Hopfield, J.J. (1982). Neural networks and physical systems with emergent collective computational
abilities. PNAS.
researchor_mental_model_id: attractors_and_basins
status: seed
- id: renormalization_group
name: Renormalization Group
year: 1971
origin: Wilson; Kadanoff (block-spin 1966)
signature:
operation: transform
domain: scalar_field
codomain: scalar_field
objective_family: none
meso_type: energy_model
macro_type: hamiltonian_system
canonical_reference: Wilson, K.G. (1971). Renormalization group and critical phenomena. Phys. Rev. B.
researchor_mental_model_id: scale_invariance
status: seed
- id: langevin_dynamics
name: Langevin Dynamics
year: 1908
origin: Langevin; adapted to sampling by Parisi (1981)
signature:
operation: sample
domain: scalar_field
codomain: distribution
objective_family: energy
meso_type: dynamical_system
macro_type: stochastic_process
canonical_reference: Langevin, P. (1908). Sur la théorie du mouvement brownien.
researchor_artifact_id: brownian_motion
status: seed
- id: hamiltonian_monte_carlo
name: Hamiltonian Monte Carlo
year: 1987
origin: Duane, Kennedy, Pendleton & Roweth; Neal (2011 MCMC handbook)
signature:
operation: sample
domain: distribution
codomain: sequence
objective_family: energy
meso_type: dynamical_system
macro_type: hamiltonian_system
canonical_reference: Neal, R.M. (2011). MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo.
status: seed
- id: diffusion_sde
name: Diffusion Process / Reverse-Time SDE
year: 2015
origin: Sohl-Dickstein et al.; Ho, Jain & Abbeel (DDPM 2020); Song et al. (SDE 2021)
signature:
operation: sample
domain: distribution
codomain: distribution
objective_family: none
meso_type: diffusion_process
macro_type: stochastic_process
canonical_reference: Song, Y. et al. (2021). Score-based generative modeling through stochastic differential equations.
ICLR.
researchor_artifact_id: brownian_motion
researchor_mental_model_id: irreversibility
status: seed
canonical_arxiv_id: '2011.13456'
- id: wasserstein_distance
name: Wasserstein Distance / Earth Mover's Distance
year: 1781
origin: Monge; Kantorovich (1942)
signature:
operation: match
domain: distribution
codomain: scalar
objective_family: none
meso_type: optimal_transport
macro_type: optimization
canonical_reference: Kantorovich, L.V. (1942). On the translocation of masses.
status: seed
- id: sinkhorn_algorithm
name: Sinkhorn-Knopp Algorithm / Entropic OT
year: 1967
origin: Sinkhorn & Knopp; Cuturi (2013) for ML
signature:
operation: match
domain: distribution
codomain: matrix
objective_family: divergence
meso_type: optimal_transport
macro_type: optimization
canonical_reference: 'Cuturi, M. (2013). Sinkhorn distances: lightspeed computation of optimal transport. NeurIPS.'
status: seed
canonical_arxiv_id: '1306.0895'
- id: kantorovich_dual
name: Kantorovich Duality
year: 1942
origin: Kantorovich
signature:
operation: maximize
domain: distribution
codomain: scalar
objective_family: none
meso_type: optimal_transport
macro_type: optimization
canonical_reference: 'Villani, C. (2008). Optimal Transport: Old and New. Springer.'
status: seed
- id: gradient_descent
name: Gradient Descent
year: 1847
origin: Cauchy
signature:
operation: minimize
domain: scalar_field
codomain: vector
objective_family: none
meso_type: none
macro_type: optimization
canonical_reference: Cauchy, A. (1847). Méthode générale pour la résolution des systèmes d'équations simultanées.
researchor_artifact_id: gradient_descent
status: seed
- id: sgd
name: Stochastic Gradient Descent
year: 1951
origin: Robbins & Monro
signature:
operation: minimize
domain: scalar_field
codomain: vector
objective_family: none
meso_type: none
macro_type: optimization
canonical_reference: Robbins, H. & Monro, S. (1951). A stochastic approximation method.
researchor_artifact_id: stochastic_gradient_descent
status: seed
- id: lagrange_multiplier
name: Constrained Optimization (Lagrange Multiplier)
year: 1788
origin: Lagrange
signature:
operation: minimize
domain: scalar_field
codomain: vector
objective_family: none
meso_type: none
macro_type: optimization
canonical_reference: Lagrange, J.-L. (1788). Mécanique Analytique.
status: seed
- id: proximal_gradient
name: Proximal Gradient Method
year: 2005
origin: Combettes & Wajs; Beck & Teboulle (FISTA 2009)
signature:
operation: minimize
domain: scalar_field
codomain: vector
objective_family: none
meso_type: none
macro_type: optimization
canonical_reference: Beck, A. & Teboulle, M. (2009). A fast iterative shrinkage-thresholding algorithm. SIAM J. Imaging
Sci.
status: seed
- id: adam
name: Adam Optimizer
year: 2014
origin: Kingma & Ba
signature:
operation: minimize
domain: scalar_field
codomain: vector
objective_family: none
meso_type: none
macro_type: optimization
canonical_reference: 'Kingma, D.P. & Ba, J. (2015). Adam: a method for stochastic optimization. ICLR.'
status: seed
canonical_arxiv_id: '1412.6980'
- id: softmax_attention
name: Softmax Attention / Weighted Aggregation
year: 2014
origin: Bahdanau, Cho & Bengio; Vaswani et al. (Transformer 2017)
signature:
operation: aggregate
domain: sequence
codomain: vector
objective_family: none
meso_type: none
macro_type: none
canonical_reference: Vaswani, A. et al. (2017). Attention is all you need. NeurIPS.
status: seed
canonical_arxiv_id: '1706.03762'
- id: residual_connection
name: Residual Connection / Skip Connection
year: 2016
origin: He, Zhang, Ren & Sun; earlier in Hochreiter & Schmidhuber (LSTM 1997)
signature:
operation: transform
domain: vector
codomain: vector
objective_family: none
meso_type: none
macro_type: none
canonical_reference: He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. CVPR.
status: seed
canonical_arxiv_id: '1512.03385'
- id: batch_normalization
name: Batch Normalization
year: 2015
origin: Ioffe & Szegedy
signature:
operation: transform
domain: vector
codomain: vector
objective_family: none
meso_type: none
macro_type: none
canonical_reference: 'Ioffe, S. & Szegedy, C. (2015). Batch normalization: accelerating deep network training. ICML.'
status: seed
canonical_arxiv_id: '1502.03167'
- id: vae
name: Variational Autoencoder
year: 2013
origin: Kingma & Welling; Rezende, Mohamed & Wierstra
signature:
operation: transform
domain: vector
codomain: distribution
objective_family: divergence
meso_type: variational
macro_type: statistical_inference
canonical_reference: Kingma, D.P. & Welling, M. (2014). Auto-encoding variational Bayes. ICLR.
status: seed
canonical_arxiv_id: '1312.6114'
- id: gan
name: Generative Adversarial Network
year: 2014
origin: Goodfellow et al.
signature:
operation: minimize
domain: distribution
codomain: distribution
objective_family: adversarial
meso_type: game_theoretic
macro_type: optimization
canonical_reference: Goodfellow, I.J. et al. (2014). Generative adversarial nets. NeurIPS.
researchor_mental_model_id: nash_equilibrium
status: seed
canonical_arxiv_id: '1406.2661'
- id: contrastive_learning
name: Contrastive Learning
year: 2005
origin: Chopra, Hadsell & LeCun (Siamese, 2005); Hadsell et al. (dimensionality reduction 2006)
signature:
operation: minimize
domain: vector
codomain: scalar
objective_family: energy
meso_type: joint_embedding
macro_type: optimization
canonical_reference: Hadsell, R., Chopra, S., & LeCun, Y. (2006). Dimensionality reduction by learning an invariant mapping.
CVPR.
researchor_mental_model_id: signal_vs_noise
status: seed
- id: knowledge_distillation
name: Knowledge Distillation
year: 2015
origin: Hinton, Vinyals & Dean
signature:
operation: minimize
domain: distribution
codomain: distribution
objective_family: divergence
meso_type: none
macro_type: optimization
canonical_reference: Hinton, G., Vinyals, O., & Dean, J. (2015). Distilling the knowledge in a neural network. NeurIPS workshop.
status: seed
canonical_arxiv_id: '1503.02531'
- id: layer_normalization
name: Layer Normalization
year: 2016
origin: Ba, Kiros & Hinton
signature:
operation: transform
domain: vector
codomain: vector
objective_family: none
meso_type: none
macro_type: none
canonical_reference: Ba, J.L., Kiros, J.R., & Hinton, G.E. (2016). Layer normalization. arXiv:1607.06450.
status: seed
canonical_arxiv_id: '1607.06450'
- id: ridge_regression
name: Ridge Regression (L2 Regularization)
year: 1970
origin: Hoerl & Kennard; Tikhonov (1943)
signature:
operation: minimize
domain: vector
codomain: scalar
objective_family: none
meso_type: none
macro_type: optimization
canonical_reference: 'Hoerl, A.E. & Kennard, R.W. (1970). Ridge regression: biased estimation for nonorthogonal problems.'
status: seed
- id: lasso
name: LASSO (L1 Regularization)
year: 1996
origin: Tibshirani
signature:
operation: minimize
domain: vector
codomain: scalar
objective_family: none
meso_type: none
macro_type: optimization
canonical_reference: Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. JRSS-B.
status: seed
- id: elastic_net
name: Elastic Net
year: 2005
origin: Zou & Hastie
signature:
operation: minimize
domain: vector
codomain: scalar
objective_family: none
meso_type: none
macro_type: optimization
canonical_reference: Zou, H. & Hastie, T. (2005). Regularization and variable selection via the elastic net. JRSS-B.
status: seed
- id: spectral_clustering
name: Spectral Clustering
year: 2000
origin: Shi & Malik (normalized cuts); Ng, Jordan & Weiss (2002)
signature:
operation: decompose
domain: graph
codomain: assignment
objective_family: none
meso_type: spectral_method
macro_type: eigenvalue_problem
canonical_reference: 'Ng, A.Y., Jordan, M.I., & Weiss, Y. (2002). On spectral clustering: analysis and an algorithm. NeurIPS.'
researchor_artifact_id: laplacian_matrix
status: seed
- id: pagerank
name: PageRank
year: 1998
origin: Page, Brin, Motwani & Winograd
signature:
operation: propagate
domain: graph
codomain: vector
objective_family: none
meso_type: spectral_method
macro_type: eigenvalue_problem
canonical_reference: 'Page, L. et al. (1999). The PageRank citation ranking: bringing order to the web.'
researchor_artifact_id: adjacency_matrix
researchor_mental_model_id: network_centrality
status: seed
- id: fourier_transform
name: Fourier Transform / Spectral Decomposition
year: 1822
origin: Fourier; Cooley & Tukey (FFT 1965)
signature:
operation: decompose
domain: sequence
codomain: sequence
objective_family: none
meso_type: spectral_method
macro_type: none
canonical_reference: Fourier, J.B.J. (1822). Théorie analytique de la chaleur.
researchor_mental_model_id: signal_vs_noise
status: seed