Michael Biehl

A summary is presented of the statistical mechanical theory of learning a rule with a neural network, a rapidly advancing area which is closely related to other inverse problems frequently encountered by physicists. By emphasizing the relationship between neural networks and strongly interacting physical systems, such as spin glasses, the authors show how learning theory has provided a workshop in which to develop new, exact analytical techniques.

CONTEXT: Adrenal tumors have a prevalence of around 2% in the general population. Adrenocortical carcinoma (ACC) is rare but accounts for 2-11% of incidentally discovered adrenal masses. Differentiating ACC from adrenocortical adenoma (ACA) represents a diagnostic challenge in patients with adrenal incidentalomas, with tumor size, imaging, and even histology all providing unsatisfactory predictive values. OBJECTIVE: Here we developed a novel steroid metabolomic approach, mass spectrometry-based steroid profiling followed by machine learning analysis, and examined its diagnostic value for the detection of adrenal malignancy. DESIGN: Quantification of 32 distinct adrenal derived steroids was carried out by gas chromatography/mass spectrometry in 24-h urine samples from 102 ACA patients (age range 19-84 yr) and 45 ACC patients (20-80 yr). Underlying diagnosis was ascertained by histology and metastasis in ACC and by clinical follow-up [median duration 52 (range 26-201) months] without evidence of metastasis in ACA. Steroid excretion data were subjected to generalized matrix learning vector quantization (GMLVQ) to identify the most discriminative steroids. RESULTS: Steroid profiling revealed a pattern of predominantly immature, early-stage steroidogenesis in ACC. GMLVQ analysis identified a subset of nine steroids that performed best in differentiating ACA from ACC. Receiver-operating characteristics analysis of GMLVQ results demonstrated sensitivity = specificity = 90% (area under the curve = 0.97) employing all 32 steroids and sensitivity = specificity = 88% (area under the curve = 0.96) when using only the nine most differentiating markers. CONCLUSIONS: Urine steroid metabolomics is a novel, highly sensitive, and specific biomarker tool for discriminating benign from malignant adrenal tumors, with obvious promise for the diagnostic work-up of patients with adrenal incidentalomas.

We propose a new matrix learning scheme to extend relevance learning vector quantization (RLVQ), an efficient prototype-based classification algorithm, toward a general adaptive metric. By introducing a full matrix of relevance factors in the distance measure, correlations between different features and their importance for the classification scheme can be taken into account and automated, and general metric adaptation takes place during training. In comparison to the weighted Euclidean metric used in RLVQ and its variations, a full matrix is more powerful to represent the internal structure of the data appropriately. Large margin generalization bounds can be transferred to this case, leading to bounds that are independent of the input dimensionality. This also holds for local metrics attached to each prototype, which corresponds to piecewise quadratic decision boundaries. The algorithm is tested in comparison to alternative learning vector quantization schemes using an artificial data set, a benchmark multiclass problem from the UCI repository, and a problem from bioinformatics, the recognition of splice sites for C. elegans.