Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The development of science and technology promotes the constant changes of consumer finance, but also brings some financial credit risks. In particular, with the continuous development of Internet finance, financial credit risk is increasingly difficult to control. Based on machine learning algorithm, this study improved the machine learning algorithm and named it MLIA algorithm. Meanwhile, this study decomposes the objective function into weighted sums of several basis functions. This study uses three typical test functions to compare the performance of MLIA prediction algorithm and logistic prediction algorithm. Simultaneously, this study analyzes the performance of MLIA financial credit risk prediction model by taking the data of an Internet financial company as an example. In addition, this study used the AUC (area under curve) value as a specific indicator of model performance verification. Research shows that machine learning has a good predictive effect on MLIA financial credit risk prediction and can provide theoretical reference for subsequent related research.

Financial credit risk prediction in internet finance driven by machine learning

Despite its success in a wide range of applications, characterizing the generalization properties of stochastic gradient descent (SGD) in non-convex deep learning problems is still an important challenge. While modeling the trajectories of SGD via stochastic differential equations (SDE) under heavy-tailed gradient noise has recently shed light over several peculiar characteristics of SGD, a rigorous treatment of the generalization properties of such SDEs in a learning theoretical framework is still missing. Aiming to bridge this gap, in this paper, we prove generalization bounds for SGD under the assumption that its trajectories can be well-approximated by a \emph{Feller process}, which defines a rich class of Markov processes that include several recent SDE representations (both Brownian or heavy-tailed) as its special case. We show that the generalization error can be controlled by the \emph{Hausdorff dimension} of the trajectories, which is intimately linked to the tail behavior of the driving process. Our results imply that heavier-tailed processes should achieve better generalization; hence, the tail-index of the process can be used as a notion of "capacity metric". We support our theory with experiments on deep neural networks illustrating that the proposed capacity metric accurately estimates the generalization error, and it does not necessarily grow with the number of parameters unlike the existing capacity metrics in the literature.

/pdf/hausdorff-dimension-heavy-tails-and-generalization-in-neural-1lf5wmyubg.pdf

Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks

Data Mining and Automated Learning- Clustering by Similarity in an Auxiliary Space- Analyses on the Generalised Lotto-Type Competitive Learning- Extended K-means with an Efficient Estimation of the Number of Clusters- An Interactive Approach to Building Classiffication Models by Clustering and Cluster Validation- A New Distributed Algorithm for Large Data Clustering- A NEW NONHIERARCHICAL CLUSTERING PROCEDURE FOR SYMBOLIC OBJECTS- Quantization of Continuous Input Variables for Binary Classification- Information-Based Classification by Aggregating Emerging Patterns- Boosting the Margin Distribution- Detecting a Compact Decision Tree Based on an Appropriate Abstraction- A New Algorithm to Select Learning Examples from Learning Data- Data Ranking Based on Spatial Partitioning- Logical Decision Rules: Teaching C45 to Speak Prolog- Visualisation of Temporal Interval Association Rules- Lithofacies Characteristics Discovery from Well Log Data Using Association Rules- Fuzzy Hydrocyclone Modelling for Particle Separation Using Fuzzy Rule Interpolation- A Data-Driven Fuzzy Approach to Robot Navigation Among Moving Obstacles- Best Harmony Learning- Observational Learning with Modular Networks- Finding Essential Attributes in Binary Data- A Heuristic Optimal Reduct Algorithm- A Note on Learning Automata Based Schemes for Adaptation of BP Parameters- A Note on Covariances for Categorical Data- A General Class of Neural Networks for Principal Component Analysis and Factor Analysis- Generalised Canonical Correlation Analysis- Integrating KPCA with an Improved Evolutionary Algorithm for Knowledge Discovery in Fault Diagnosis- Temporal Data Mining Using Multilevel-Local Polynomial Models- First Experiments for Mining Sequential Patterns on Distributed Sites with Multi-Agents- Nonlinear and Noisy Time Series Prediction Using a Hybrid Nonlinear Neural Predictor- Genetic Programming Prediction of Solar Activity- Interpretation of the Richardson Plot in Time Series Representation- Financial Engineering- Wavelet Methods in PDE Valuation of Financial Derivatives- Fast Algorithms for Computing Corporate Default Probabilities- Variance-Penalized Reinforcement Learning for Risk-Averse Asset Allocation- Applying Mutual Information to Adaptive Mixture Models- Stability Analysis of Financial Ratios- Modeling of the German Yield Curve by Error Correction Neural Networks- Feature Selection for Support Vector Machines in Financial Time Series Forecasting- ?-Descending Support Vector Machines for Financial Time Series Forecasting- Classifying Market States with WARS- "Left Shoulder"Data Mining and Automated Learning- Clustering by Similarity in an Auxiliary Space- Analyses on the Generalised Lotto-Type Competitive Learning- Extended K-means with an Efficient Estimation of the Number of Clusters- An Interactive Approach to Building Classiffication Models by Clustering and Cluster Validation- A New Distributed Algorithm for Large Data Clustering- A NEW NONHIERARCHICAL CLUSTERING PROCEDURE FOR SYMBOLIC OBJECTS- Quantization of Continuous Input Variables for Binary Classification- Information-Based Classification by Aggregating Emerging Patterns- Boosting the Margin Distribution- Detecting a Compact Decision Tree Based on an Appropriate Abstraction- A New Algorithm to Select Learning Examples from Learning Data- Data Ranking Based on Spatial Partitioning- Logical Decision Rules: Teaching C45 to Speak Prolog- Visualisation of Temporal Interval Association Rules- Lithofacies Characteristics Discovery from Well Log Data Using Association Rules- Fuzzy Hydrocyclone Modelling for Particle Separation Using Fuzzy Rule Interpolation- A Data-Driven Fuzzy Approach to Robot Navigation Among Moving Obstacles- Best Harmony Learning- Observational Learning with Modular Networks- Finding Essential Attributes in Binary Data- A Heuristic Optimal Reduct Algorithm- A Note on Learning Automata Based Schemes for Adaptation of BP Parameters- A Note on Covariances for Categorical Data- A General Class of Neural Networks for Principal Component Analysis and Factor Analysis- Generalised Canonical Correlation Analysis- Integrating KPCA with an Improved Evolutionary Algorithm for Knowledge Discovery in Fault Diagnosis- Temporal Data Mining Using Multilevel-Local Polynomial Models- First Experiments for Mining Sequential Patterns on Distributed Sites with Multi-Agents- Nonlinear and Noisy Time Series Prediction Using a Hybrid Nonlinear Neural Predictor- Genetic Programming Prediction of Solar Activity- Interpretation of the Richardson Plot in Time Series Representation- Financial Engineering- Wavelet Methods in PDE Valuation of Financial Derivatives- Fast Algorithms for Computing Corporate Default Probabilities- Variance-Penalized Reinforcement Learning for Risk-Averse Asset Allocation- Applying Mutual Information to Adaptive Mixture Models- Stability Analysis of Financial Ratios- Modeling of the German Yield Curve by Error Correction Neural Networks- Feature Selection for Support Vector Machines in Financial Time Series Forecasting- ?-Descending Support Vector Machines for Financial Time Series Forecasting- Classifying Market States with WARS- "Left Shoulder" Detection in Korea Composite Stock Price Index Using an Auto-Associative Neural Network- Intelligent Agents- A Computational Framework for Convergent Agents- Multi-agent Integer Programming- Building an Ontology for Financial Investment- A Multi-Agent Negotiation Algorithm for Load Balancing in CORBA-Based Environment- Existence of Minority in Multi-Agent Systems using Voronoi Tessellation- Combining Exploitation-Based and Exploration-Based Approach in Reinforcement Learning- A Probabilistic Agent Approach to the Trafic Jam Problem- Round-Table Architecture for Communication in Multi-agent Softbot Systems- Mobile Agents for Reliable Migration in Networks- Internet Applications- A Construction of the Adapted Ontology Server in EC- A Design and Implementation of Cyber Banking Process and Settlement System for Internet Commerce- A Shopping Agent That Automatically Constructs Wrappers for Semi-Structured Online Vendors- Real-time Web Data Mining and Visualisation- Web Guide: Filtering and Constraining Site Browsing through Web Walker Techniques- Topic Spotting on News Articles with Topic Repository by Controlled Indexing- Validating the Behavior of Self-Interested Agents in an Information Market Scenario- Discovering User Behavior Patterns in Personalized Interface Agents- An Agent-Based Personalized Search on a Multi-search Engine Based on Internet Search Service- A Case-Based Transformation from HTML to XML- Persistent DOM: An architecture for XML repositories in relational databases- Multimedia Processing- Automatic News Video Caption Extraction and Recognition- Advanced Multilevel Successive Elimination Algorithms for Motion Estimation in Video Coding- News Content Highlight via Fast Caption Text Detection on Compressed Video- Texture-based Text Location for Video Indexing- Video Segmentation by Two Measures and Two Thresholds- Ink Retrieval from Handwritten Documents- An Off-Line Recognizer for Hand-Written Chinese Characters- Bayesian Learning for Image Retrieva Using Multiple Features- A Content-Based Image Retrieval Method Using Third- Order Color Feature Relations- Hierarchical Discriminant Regression for Incremental and Real-Time Image Classification- Distinguishing Real and Virtual Edge Intersection in Pairs of Uncalibrated Images- Stereo Correspondence Using GA-Based Segmentation- Special Sessions- How Adaptive Agents in Stock Market Perform in the Presence of Random News: A Genetic Algorithm Approach- Learning of Virtual Dealers in an Artificial Market: Comparison with Interview Data- Toward an Agent-Based Computational Modeling of Bargaining Strategies in Double Auction Markets with Genetic Programming- Combining Ordinal Financial Predictions with Genetic Programming- Applying Independent Component Analysis to Factor Model in Finance- Web-Based Cluster Analysis System for China and Hong Kong's Stock Market- Arbitrage-Free Asset Pricing in General State Space- A Tabu Search Based Algorithm for Clustering Categorical Data Sets- A New Methodology to Compare Algorithms

Intelligent data engineering and automated learning - IDEAL 2000 : data mining, financial engineering, and intelligent agents : second International Conference, Shatin, N.T., Hong Kong, China, December 13-15, 2000 : proceedings

https://escholarship.org/content/qt3bc4p075/qt3bc4p075.pdf?t=lnpw9c

Experience, generations, and limits in machine learning

We present learning of figures, nonempty compact sets in Euclidean space, based on Gold's learning model aiming at a computable foundation for binary classification of multivariate data. Encoding real vectors with no numerical error requires infinite sequences, resulting in a gap between each real vector and its discretized representation used for the actual machine learning process. Our motivation is to provide an analysis of machine learning problems that explicitly tackles this aspect which has been glossed over in the literature on binary classification as well as in other machine learning tasks such as regression and clustering. In this paper, we amalgamate two processes: discretization and binary classification. Each learning target, the set of real vectors classified as positive, is treated as a figure. A learning machine receives discretized vectors as input data and outputs a sequence of discrete representations of the target figure in the form of self-similar sets, known as fractals. The generalization error of each output is measured by the Hausdorff metric. Using this learning framework, we reveal a hierarchy of learnable classes under various learning criteria in the track of traditional analysis based on Gold's learning model, and show a mathematical connection between machine learning and fractal geometry by measuring the complexity of learning using the Hausdorff dimension and the VC dimension. Moreover, we analyze computability aspects of learning of figures using the framework of Type-2 Theory of Effectivity (TTE).

/pdf/learning-figures-with-the-hausdorff-metric-by-fractals-2m1xuzkh23.pdf

Learning figures with the Hausdorff metric by fractals--towards computable binary classification

We combine traditional studies of inductive inference and classical continuous mathematics to produce a study of learning real-valued functions. We consider two possible ways to model the learning by example of functions with domain and range the real numbers. The first approach considers functions as represented by computable analytic functions. The second considers arbitrary computable functions of recursive real numbers. In each case we find natural examples of learnable classes of functions and unlearnable classes of functions.

Inductive inference of recursive real-valued functions

In this paper, we investigate prediction of recursive real-valued functions from finite examples by extending the framework of inductive inference of recursive real-valued functions to be a more realistic one. First, we propose a finite prediction machine, which is a procedure that requests finite examples of a recursive real-valued function h and a datum of a real number x, and that outputs a datum of h(x). Then, we formulate finite prediction of recursive real-valued functions and investigate the power of it. Furthermore, for a fixed rational closed interval I, we show that the class of all finitely predictable sets of recursive real-valued functions coincides with the class of all inferable sets of recursive real-valued functions in the limit, that is, ${\sc RealFP}_{\emph I}={\sc RealEx}_{\emph I}$.

Prediction of recursive real-valued functions from finite examples

In this paper we investigate the inductive inference of recursive real-valued functions from data. A recursive real-valued function is regarded as a computable interval mapping. The learning model we consider in this paper is an extension of Gold's inductive inference. We first introduce some criteria for successful inductive inference of recursive real-valued functions. Then we show a recursively enumerable class of recursive real-valued functions which is not inferable in the limit. This should be an interesting contrast to the result by Wiehagen (1976, Elektronische Informationsverarbeitung und Kybernetik, Vol. 12, pp. 93--99) that every recursively enumerable subset of recursive functions from N to N is consistently inferable in the limit. We also show that every recursively enumerable class of recursive real-valued functions on a fixed rational interval is consistently inferable in the limit. Furthermore, we show that our consistent inductive inference coincides with the ordinary inductive inference, when we deal with recursive real-valued functions on a fixed closed rational interval. Copyright 2001 Elsevier Science B.V. All rights reserved.

A comparison of identification criteria for inductive inference of recursive real-valued functions

Criteria for inductive inference with mind changes and anomalies of recursive real-valued functions

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