{ "_id": "6aca924afe5cc25786e8ba2d", "Package": "BsplineQuantReg", "Type": "Package", "Title": "'Constrained Quantile Regression with B-Splines'", "Version": "0.2.6", "Date": "2026-07-26", "Authors@R": "person(\"Alexandre\", \"Abbes\", email = \"alexandre.abbes@proton.me\", role = c(\"aut\", \"cre\"))", "Description": "Quantile regression with B-splines under shape\nconstraints. The initial version with cubic splines is now\naugmented with splines of degree 1 to 4. Constraints for\ndegrees 3 (monotone) and 4 (monotone and convex) use the\nKarlin-Studden SOCP characterization for the sign of the\npolynomial, while other constraints applied at the knots are\nadded as linear problems. The method for cubic splines is\ndescribed in 'Abbes (2025)' .\nOther formulations are simple consequences of the other given\nreferences. All B-spline and polynomial functions have been\nrewritten for consistency. This package provides an original\nB-spline library for conversion between PP-form and B-spline\nrepresentation, evaluation, differentiation, callable and\nnon-callable objects, print human readable pp forms, view\nbasis, all based on \"De Boor\\'s\" theory. It also extends to\nmultiple knots to catch up singularities. This feature is\nrobust in the package including for constrained regression.\nThis R implementation is intended for demonstration and\nprototyping. An equivalent Python package is available at\n.", "License": "GPL-3", "URL": "https://github.com/alexandreabbes/BsplineQuantReg", "BugReports": "https://github.com/alexandreabbes/BsplineQuantReg/issues", "VignetteBuilder": "knitr", "Encoding": "UTF-8", "Config/roxygen2/version": "8.1.0", "Config/pak/sysreqs": "cmake libgmp3-dev make pkg-config libclang-dev", "Repository": "https://alexandreabbes.r-universe.dev", "Date/Publication": "2026-10-10 19:14:59 UTC", "RemoteUrl": "https://github.com/alexandreabbes/bsplinequantreg", "RemoteRef": "HEAD", "RemoteSha": "3e6d51b50facd364ec17be37aebf951f9e26d7bc", "NeedsCompilation": "no", "Packaged": { "Date": "2026-10-10 19:21:24 UTC", "User": "root" }, "Author": "Alexandre Abbes [aut, cre]", "Maintainer": "Alexandre Abbes ", "_user": "alexandreabbes", "_type": "src", "_file": "BsplineQuantReg_0.2.6.tar.gz", "_fileid": "https://r2.ropensci.org/44adb2a3123115593622135ea6cd9b76fa89659520c8a1313ed53334a687355e", "_filesize": 2677969, "_sha256": 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Polynomials are expressed in the canonical basis Uses De Boor's recursion formula.", "topics": [ "Bspline_base" ] }, { "page": "Bspline_base_deriv", "title": "Differentiate a B-spline basis", "topics": [ "Bspline_base_deriv" ] }, { "page": "Bspline_deriv", "title": "Compute derivative coefficients of a B-spline", "topics": [ "Bspline_deriv" ] }, { "page": "bspline_to_deriv_coeffs_cubic", "title": "normalized first and second derivative coefficients on each interval. for a cubic B-spline basis", "topics": [ "bspline_to_deriv_coeffs_cubic" ] }, { "page": "bspline_to_deriv_coeffs_lin", "title": "Derivative coefficients for linear B-spline Computes normalized first derivative coefficients for linear B-splines. For linear splines, the derivative is constant on each interval.", "topics": [ "bspline_to_deriv_coeffs_lin" ] }, { "page": "bspline_to_deriv_coeffs_quad", "title": "quadratic B-spline derivative coefficients", "topics": [ "bspline_to_deriv_coeffs_quad" ] }, { "page": "bspline_to_deriv_coeffs_quart", "title": "Computes normalized first, second, and third derivative coefficients for quartic B-splines on each interval.", "topics": [ "bspline_to_deriv_coeffs_quart" ] }, { "page": "Bsplinetopp", "title": "Convert a B-spline to Piecewise Polynomial (PP) form", "topics": [ "Bsplinetopp" ] }, { "page": "change_polynomial_base_taylor", "title": "Change polynomial basis (Taylor expansion)", "topics": [ "change_polynomial_base_taylor" ] }, { "page": "evalpp", "title": "Evaluates a piecewise polynomial (PP form) function at given points.", "topics": [ "evalpp" ] }, { "page": "get_parameters", "title": "Get parameters from a callable spline or a callable pp object", "topics": [ "get_parameters" ] }, { "page": "make_spline", "title": "Create a callable spline object", "topics": [ "make_spline" ] }, { "page": "makpp", "title": "Build a piecewise polynomial (PP) form", "topics": [ "makpp" ] }, { "page": "poly_eval", "title": "Evaluate polynomial", "topics": [ "poly_eval" ] }, { "page": "polyadd", "title": "Polynomial addition", "topics": [ "polyadd" ] }, { "page": "polyderiv", "title": "Polynomial derivative Computes the derivative of order 'der' of a polynomial.", "topics": [ "polyderiv" ] }, { "page": "polymul", "title": "Polynomial multiplication", "topics": [ "polymul" ] }, { "page": "print.callable_pp", "title": "Print method for callable_pp objects", "topics": [ "print.callable_pp" ] }, { "page": "print.callable_spline", "title": "Print method for callable spline", "topics": [ "print.callable_spline" ] }, { "page": "print.non_callable_pp", "title": "Print method for non_callable_pp objects", "topics": [ "print.non_callable_pp" ] }, { "page": "print.non_callable_spline", "title": "Print method for non_callable_spline results", "topics": [ "print.non_callable_spline" ] }, { "page": "quantile_spline", "title": "Unified Quantile Regression with B-Splines of Any Degree (1 to 4)", "topics": [ "quantile_spline" ] }, { "page": "reduce_pol", "title": "Reduce polynomial", "topics": [ "reduce_pol" ] }, { "page": "setup_solver", "title": "Vérifier et configurer le solveur CVXR", "topics": [ "setup_solver" ] }, { "page": "show_poly", "title": "Displays the equation of a polynomial in a given basis", "topics": [ "show_poly" ] }, { "page": "show_pp", "title": "Display Piecewise Polynomial (PP) in a human readble form", "topics": [ "show_pp" ] }, { "page": "Spline_der_knot", "title": "Derivatives at knot of a B-spline", "topics": [ "Spline_der_knot" ] }, { "page": "spline_eval", "title": "Evaluate a B-spline", "topics": [ "spline_eval" ] }, { "page": "SplineConstantQuant", "title": "' Performs quantile/mean regression using constant B-splines with monotonicity constraints. No solver is needed, since for the degree 0, the B-splines in the basis are independent piece-wise constants.", "topics": [ "SplineConstantQuant" ] }, { "page": "SplineConstQuantRegBs1", "title": "Wrapper function for linear spline quantile regression", "topics": [ "SplineConstQuantRegBs1" ] }, { "page": "SplineConstQuantRegBs2", "title": "Wrapper function for quadratic spline quantile regression Previous version notation style This is a convenience wrapper for SplineQuadraticQuant.", "topics": [ "SplineConstQuantRegBs2" ] }, { "page": "SplineConstQuantRegBs3", "title": "Wrapper function for Cubic spline quantile regression", "topics": [ "SplineConstQuantRegBs3" ] }, { "page": "SplineConstQuantRegBs4", "title": "Wrapper function for quartic spline quantile regression", "topics": [ "SplineConstQuantRegBs4" ] }, { "page": "SplineCubicQuant", "title": "Constrained quantile regression with cubic splines Performs quantile regression using cubic B-splines, with optional monotonicity constraints (via Karlin-Studden) and convexity constraints.", "topics": [ "SplineCubicQuant" ] }, { "page": "SplineLinearQuant", "title": "Quantile regression with linear splines and monotonicity constraints", "topics": [ "SplineLinearQuant" ] }, { "page": "SplinePolynQuant", "title": "Quantile regression with general polynomial splines and shape constraints", "topics": [ "SplinePolynQuant" ] }, { "page": "SplineQuadraticQuant", "title": "Quantile regression with quadratic splines and shape constraints", "topics": [ "SplineQuadraticQuant" ] }, { "page": "SplineQuarticQuant", "title": "Quantile regression with quartic splines and shape constraints", "topics": [ "SplineQuarticQuant" ] }, { "page": "test_karlin_simple", "title": "Comprehensive test function", "topics": [ "test_karlin_simple" ] }, { "page": "view_basis", "title": "Visualize a B-spline functions basis Visualize a B-spline basis Plots all basis functions of a B-spline basis with improved styling.", "topics": [ "view_basis" ] } ], "_readme": "https://github.com/alexandreabbes/bsplinequantreg/raw/HEAD/README.md", "_rundeps": [ "backports", "checkmate", "clarabel", "cli", "CVXR", "ECOSolveR", "gmp", "highs", "lattice", "Matrix", "osqp", "Rcpp", "RcppEigen", "S7", "scs", "slam" ], "_vignettes": [ { "source": "bspline_basis_manipulation.Rmd", "filename": "bspline_basis_manipulation.html", "title": "B-spline Basis Manipulation", "author": "Alexandre Abbes", "engine": "knitr::rmarkdown", "headings": [ "Introduction", "Building a B-spline Basis", "Basic Construction", "Visualizing the Basis", "Understanding the Extended Knot Sequence", "Visualizing B-spline Bases", "Visualizing a B-spline Basis", "Visualizing Different Degrees", "Customizing Visualization", "Differentiating a B-spline Basis", "Visualizing Derivative Bases", "Differentiating a B-spline Function", "Method 1: Using spline_eval() with der Parameter", "Method 2: Using Bspline_deriv() to Get Derivative Coefficients", "Method 3: Step-by-step evaluation using basis derivatives", "1. Compute the derivative basis", "2. Evaluate the basis at points using bs_direct", "3. Use matrix multiplication with coefficients", "PP-form Conversion", "Callable PP Objects", "Callable Splines", "Creating Callable Splines", "Non-Callable Splines", "Getting Parameters", "Advanced: Knot Multiplicity and Regularity", "Creating B-splines with Multiple Knots", "Effect of Multiplicity on Regularity", "Derivatives at Knots", "Simple Example: Coherence of Derivative Evaluation Methods (Degree 5)", "Summary" ], "created": "2026-08-08 20:35:13", "modified": "2026-10-07 17:06:11", "commits": 4 }, { "source": "introduction.Rmd", "filename": "introduction.html", "title": "Introduction", "engine": "knitr::rmarkdown", "headings": [ "Simple example", "Core content", "B-spline library", "Graphical user interface", "An interactive Shiny GUI is available:", "Python port" ], "created": "2026-08-07 07:25:45", "modified": "2026-10-10 19:14:59", "commits": 3 }, { "source": "polynomial_library.Rmd", "filename": "polynomial_library.html", "title": "Polynomial Library in BsplineQuantReg", "author": "Alexandre Abbes", "engine": "knitr::rmarkdown", "headings": [ "Introduction", "Basic Polynomial Operations", "Polynomial Multiplication", "Polynomial Addition", "Polynomial Evaluation", "Polynomial Differentiation", "Polynomial Reduction", "Taylor Basis Change", "Piecewise Polynomial (PP) Form", "Creating a PP Object", "Non-Callable PP Objects", "Callable PP Objects", "Create a callable PP", "Evaluate directly", "Print shows information", "Can be used in plots", "Extrapolating values", "PP with two intervals: x^2 on [0,1], 2x-1 on [1,2]", "Evaluate inside and outside the knot range", "The values at -0.5 and 2.5 are extrapolated", "Advanced: PP Form Manipulation", "Extracting a Single Interval Polynomial", "Combining PP Objects", "Visualizing PP with Basis Functions", "Comparison: PP vs B-spline", "Summary", "Displaying polynomial in a human readable form", "Basic Usage", "Canonical Basis (Default)", "Working with Local Bases", "Display in Local Basis", "Converting Between Bases", "Examples with Different Bases", "Positive and Negative Centers", "Controlling Output Format", "Number of Digits", "Working with B-splines", "Integration with show_pp()", "Summary show_pp()" ], "created": "2026-08-08 20:35:13", "modified": "2026-10-10 16:26:55", "commits": 3 }, { "source": "shape_constraints.Rmd", "filename": "shape_constraints.html", "title": "Shape Constraints with BsplineQuantReg", "author": "Alexandre Abbes", "engine": "knitr::rmarkdown", "headings": [ "Introduction", "Available Demos", "Uniform Constraints", "Monotonicity Constraints", "Convexity Constraints", "Third Derivative Constraints", "Constraints by Degree", "Partial Constraints", "Partial Monotonicity", "Partial Convexity", "Mixed Constraints", "Constraints with Multiple Knots", "Recap: Visualizing Constraint Effects", "Karlin-Studden SOCP Formulation", "Practical Considerations", "When to Use Shape Constraints", "Constraint Strength", "Choosing the Degree", "Summary" ], "created": "2026-08-07 07:25:45", "modified": "2026-10-10 16:26:55", "commits": 4 }, { "source": "theoretical_background.Rmd", "filename": "theoretical_background.html", "title": "Theoretical Background", "author": "Alexandre Abbes", "engine": "knitr::rmarkdown", "headings": [ "Introduction", "1. 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