Pseudo-inverse
A pseudoinverse is a generalized matrix inverse that provides least-squares solutions when an ordinary inverse does not exist.
Math and Architectures of Deep Learning
- How it is used
- Solves overdetermined or underdetermined linear systems and fits linear machine-learning models by minimizing error.
- How deep it goes
- Defines the normal-equation formula, explains projection geometry, and derives an SVD route while deferring direct inverse computation.
- Examples
- Uses a toy cat-brain threat-score dataset, an augmented design matrix, projection geometry, and SVD-based system solving.
- What you can do after
- Apply it via matrix formulas or SVD to obtain best-fit solutions for nonsquare linear systems.
Read how Math and Architectures of Deep Learning explains pseudo-inverse →
Experimentation for Engineers
A generalized matrix inverse that remains defined for some matrices whose ordinary inverse is undefined and agrees with the ordinary inverse when that inverse exists.
- How it is used
- Stabilizes action-specific linear regression in a contextual-bandit model built from logged user contexts and rewards.
- How deep it goes
- Defines the generalization and gives a NumPy formula, but does not derive Moore–Penrose properties or numerical algorithms.
- Examples
- Uses action-grouped samples and build_models with np.linalg.pinv(x.T@x)@x.T@y.
- What you can do after
- Apply it via NumPy to fit regression coefficients when ordinary matrix inversion may be undefined.
Read how Experimentation for Engineers explains pseudo-inverse →
Related concepts
- matrix inverseequivalent to · A matrix inverse is a matrix that, when it exists, multiplies with a square matrix to produce the identity matrix.
- linear systemaddresses · A linear system is a set of linear relationships among variables, commonly expressed as simultaneous equations or a linear transformation, for which superposition applies.
- normal equationalternative to · A normal equation is a matrix equation whose solution provides the ordinary least-squares coefficients of a linear regression model.
- singular value decompositionproduced by · Singular value decomposition is a matrix factorization that expresses a matrix as the product of orthogonal or unitary matrices and a diagonal matrix of nonnegative singular values.
- transpositionuses · Transposition is an operation that exchanges a matrix’s rows and columns or, more generally, reorders the axes of a tensor without changing its values.
- PyTorchused by · PyTorch is an open-source machine-learning framework for Python that provides tensor computation, automatic differentiation, and tools for building and training neural networks.
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