Logistic regression may be used for classification.

In order to preserve the convex nature for the loss function, a log-loss cost function has been designed for logistic regression. This cost function extremes at labels True and False.

The gradient for the loss function of logistic regression comes out to have the same form of terms as the gradient for the Least Squared Error.

More: https://www.baeldung.com/cs/gradient-descent-logistic-regression

#optimization #algebra #linearAlgebra #math #maths #mathematics #mathStodon #ML #dataScience #machineLearning #DeepLearning #neuralNetworks #NLP #modeling #modelling #models #dataDev #AIDev #regression #modelling #dataLearning #probabilities #logisticRegression #logLoss #sigmoid #classification #differentialCalculus #loss

Differential Propositional Calculus • 10

Special Classes of Propositions (cont.)

Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions.  The case for 3 variables is exemplary enough for a start.

Linear Propositions

The linear propositions, may be written as sums:

One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that

In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.

At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.

Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.

Next are the three linear propositions of rank 1, which are none other than the three basic propositions,

At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple

Resources

• Logic Syllabus
• Survey of Differential Logic

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization

Où l'on apprend que l'intégrale n'est pas une anti-dérivée (est introduite aussi la notion de manifold):

https://www.youtube.com/watch?v=1lGM5DEdMaw

PS: la notion moderne de forme différentielle est attribuable au mathématicien Français Élie Cartan (1969-1951).

#maths #DifferentialCalculus

@riewarden

The real explanation is that Michael Spivak did the cover illustrations xyrself, and published through xyr own publishing company; and there's no real reason for the covers to make sense for anyone else. They also differ from edition to edition.

Amazon tells me that you've ordered the 2nd edition, not the 3rd.

#DifferentialCalculus #textbooks #MichaelSpivak

#DifferentialLogic and #DynamicSystems • Overview
• https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

In modeling #IntelligentSystems, natural or artificial, there is a tension between #DynamicParadigms & #SymbolicParadigms.

#DynamicModels afford a system #QuantitativeDescription, charting its #TimeEvolution via #DifferentialEquations.

#SymbolicModels afford a system #QualitativeDescription, deducing its #LogicalConsequences. So far these tend to be static models, awaiting a logical analogue of #DifferentialCalculus.

I was explaining to my wife yesterday how #DifferentialCalculus gives us a way to find the #gradient of a #function at any point and to illustrate it I wrote a short routine in #Maxima to draw the #tangent to any point on a graph of a function. Here we see the example for the #quadratic and #reciprocal functions, x^2 and 1/x i.e. a #parabola and a #hyperbola respectively.

#MyWork #Gif #AnimatedGif #CCBYSA #WxMaxima #Mathematics #Maths #Calculus #Differentiation