# STATISTICAL SCIENCES FOR FINANCE | ADVANCED STATISTICAL LEARNING II

## STATISTICAL SCIENCES FOR FINANCE ADVANCED STATISTICAL LEARNING II

 0222400036 DEPARTMENT OF ECONOMICS AND STATISTICS EQF7 STATISTICAL SCIENCES FOR FINANCE 2022/2023

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2014 SPRING SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY SECS-S/01 5 30 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 MICHELE LA ROCCA T
ExamDate
ADVANCED STATISTICAL LEARNING II05/04/2023 - 14:30
ADVANCED STATISTICAL LEARNING II05/04/2023 - 14:30
Objectives
THE COURSE AIMS TO PROVIDE ADVANCED STATISTICAL LEARNING TOOLS BASED ON NEURAL NETWORK MODELS. STUDENTS WILL LEARN BOTH THE BASIC THEORETICAL CONCEPTS AND THE COMPUTATIONAL SKILLS NEEDED FOR THE SPECIFICATION AND ESTIMATION OF BOTH SHALLOW AND DEEP NEURAL NETWORKS. PARTICULAR EMPHASIS WILL BE PLACED ON THE USE OF THIS CLASS OF MODELS FOR THE STUDY OF DEPENDENCE BETWEEN STATISTICAL VARIABLES AND FOR THE STUDY AND PREDICTION OF DYNAMIC PHENOMENA, WITH A SPECIFIC FOCUS ON BIGDATA AND FINANCIAL AND INSURANCE APPLICATIONS.
CONOSCENZE E CAPACITÀ DI COMPRENSIONE
STUDENTS WILL LEARN KNOWLEDGE FOR:
–THE SPECIFICATION OF FEEDFORWARD NEURAL NETWORKS, BOTH SHALLOW AND DEEP, AND THEIR APPROXIMATION PROPERTY FOR PHENOMENA CHARACTERIZED BY HIGH NONLINEARITY
–THE USE OF LEARNING TECHNIQUES BOTH BASED ON BACKPROPAGATION (AND ITS VARIANTS) AND BASED ON EXTREME LEARNING MACHINES
–THE CHOICE AND USE OF DIFFERENT LOSS FUNCTIONS FOR BOTH CONTINUOUS AND DISCRETE DATA (BINARY, COUNT, ETC.)
–VERIFICATION AND VALIDATION OF THE ESTIMATED MODEL
–APPLICATION TO DYNAMIC PHENOMENA
–THE APPLICATION OF THESE TOOLS FOR THE SOLUTION OF THE MAIN PROBLEMS THAT MAY ARISE IN FINANCIAL AND INSURANCE APPLICATIONS
–THE USE OF SPECIFIC SOFTWARE AND STATISTICAL LANGUAGES
CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE
THE STUDENT WILL DEVELOP THE ABILITY TO:
–SPECIFY, ESTIMATE AND VALIDATE BOTH SHALLOW AND DEEP NEURAL NETWORKS.
–APPLY THIS CLASS OF MODELS TO DIFFERENT TYPES OF DATA (CONTINUOUS, DISCRETE, ETC.), TO DIFFERENT DEPENDENCY SCHEMES (REGRESSION AND TIME SERIES), TO DIFFERENT APPLICATION AREAS WITH A PARTICULAR FOCUS ON FINANCIAL AND INSURANCE PROBLEMS.
–USE THE STATISTICAL LANGUAGE R FOR THE IMPLEMENTATION OF THE MODELS COVERED BY THE COURSE
–ANALYZE AND EVALUATE INDEPENDENTLY AND CRITICALLY DOCUMENTS AND REPORTS THAT INCLUDE INFORMATION GENERATED WITH NEURAL NETWORKS, MAKING CRITICAL JUDGMENTS ON THE PARTICULAR ARCHITECTURE USED, THE INFERENCE TECHNIQUES AND PREDICTIVE MODELS BUILT AS WELL AS ON THE VALIDITY, INTERNAL AND EXTERNAL, OF THE CONCLUSIONS REACHED.
–PRESENT THE RESULTS, BOTH IN ORAL AND WRITTEN FORM, WITH LANGUAGE PROPERTIES, EFFECTIVELY AND CLEARLY.
STUDENTS WILL BE URGED TO LEARN THE LOGICAL-CONCEPTUAL STRUCTURE NECESSARY FOR THE USE OF THIS SOPHISTICATED AND COMPLEX CLASS OF MODELS, ALSO PROVIDING THE ABILITY TO LINK THE SKILLS ACQUIRED WITH THOSE LEARNED IN THE MORE RELATED STUDY COURSES.
Prerequisites
KNOWLEDGE OF NOTIONS OF MATRIX CALCULATION, BASIC PROGRAMMING, R STATISTICAL LANGUAGE, REGRESSION MODELS (AT LEAST AT INTRODUCTORY LEVEL) IS REQUIRED.
Contents
BIO-INSPIRED NEURAL MODELS AND SOME HISTORICAL NOTES ON THEIR EVOLUTION. SINGLE FEED-FORWARD NEURAL NETWORKS. UNIVERSAL APPROXIMATION THEOREMS. BACKPROPAGATION AND ITS VARIANTS. ESTIMATE OF THE MODEL USING EXTREME LEARNING MACHINES. CHOICE OF APPRORIATE LOSS FUNCTIONS. MODEL TESTING AND VALIDATION. K-FOLD CROSS-VALIDATION AND DIAGNOSTIC TESTS. GENERALIZED LINEAR MODELS BASED ON NEURAL NETWORKS. DEEP NEURAL NETWORKS. NEURAL NETWORKS FOR THE ANALYSIS AND FORECASTING OF NON-LINEAR TIME SERIES. NEURAL NETWORKS IN R . APPLICATIONS OF NEURAL NETWORKS FOR THE SOLUTION OF FINANCIAL AND INSURANCE PROBLEMS. CASE STUDIES WITH R.
Teaching Methods
THE COURSE INCLUDES 30 HOURS OF CLASSROOM TEACHING. ALTHOUGH NOT MANDATORY, GIVEN THE NATURE OF THE COURSE, ATTENDANCE IS STRONGLY RECOMMENDED.
DURING CLASSES, THEORETICAL ISSUES WILL BE ADDRESSED, CONSTANTLY SUPPORTED BY THE PRESENTATION OF CASE STUDIES THROUGH WHICH THE METHODS OF IMPLEMENTATION OF THE TECHNIQUES, THE CONTEXTS OF USE OF THE VARIOUS TOOLS AND THE POSSIBLE INTERPRETATIONS OF THE RESULTS OBTAINED WILL BE CLARIFIED. AS A CONSEQUENCE, EXERCISES WILL FORM AN INTEGRAL PART OF THE SCHEDULED LESSONS.
Verification of learning
THE STUDENT WILL BE ASSESSED DURING THE FINAL TEST TO BE HELD ON THE EXAM DATES SCHEDULED BY THE DEPARTMENT.
DURING THE FINAL TEST, THE STUDENT WILL HAVE TO TAKE A WRITTEN TEST (ASSESSED IN THIRTIETHS) AND AN ORAL TEST WHICH WILL BE HELD, TYPICALLY, IN THE DAYS IMMEDIATELY FOLLOWING. THE DATE OF THE WRITTEN TEST IS THAT SCHEDULED BY THE DEPARTMENT, THE DAY OF THE ORAL TEST IS COMMUNICATED TO THE STUDENTS AT THE END OF THE WRITTEN TEST.
THE WRITTEN TEST (DURATION OF ABOUT 2 HOURS) IS AIMED AT ASCERTAINING THE STUDENT'S ABILITY TO USE THE SOFTWARE TOOLS COVERED BY THE COURSE, TO SPECIFY, ESTIMATE AND VALIDATE NEURAL NETWORK MODELS, TO INTERPRET AND COMMENT ON THE STATISTICAL RESULTS OBTAINED. DURING THE WRITTEN TEST, THE STUDENT WILL RECEIVE AN EXAM TRACK AND WILL BE ASKED TO ANSWER 5 QUESTIONS (EACH WITH A MAXIMUM SCORE OF 6 POINTS) ON THE ENTIRE COURSE PROGRAM. THE ORAL TEST (LASTING ABOUT 30 MINUTES) CONSISTS OF AN INTERVIEW WITH QUESTIONS AND DISCUSSION OF THE WRITTEN PAPER. THE FINAL MARK (MIN 18, MAX 30 WITH POSSIBLE HONORS) IS ATTRIBUTED BY EVALUATING THE RESULTS OF THE WRITTEN AND ORAL TESTS IN WHICH THE MASTERY OF THE COURSE CONTENT WILL BE ASSESSED, APPROPRIATENESS OF THE DEFINITIONS AND THEORETICAL REFERENCES, CLARITY OF THE ARGUMENT, DOMAIN OF SPECIALIZED LANGUAGE.
Texts
LECTURE NOTES, WEB RESOURCES AND ARTICLES SUGGESTED BY THE INSTRUCTOR DURING THE COURSE WILL BE MADE AVAILABLE TO ALL ATTENDING STUDENTS

EFFECTIVE STATISTICAL LEARNING FOR ACTUARIES: NEURAL NETWORKS AND EXTENSIONS. MICHEL DENOUIT, DONATIEN HAINAUT, JULIEN TRUFIN, SPRINGER

TO RESPOND FLEXIBLY TO THE SPECIFIC NEEDS OF EACH INDIVIDUAL STUDENT, THE TEACHER CAN RECOMMEND ALTERNATIVE OR ADDITIONAL READINGS DURING THE LESSONS TO STUDENTS WHO REQUEST THEM.