This course is designed to introduce graduate students to the foundations of database systems, focusing on basics such as the relational algebra and data model, query optimization, query processing, and transactions. This is not a course on database design or SQL programming (though we will discuss these issues briefly). It is designed for students who have taken 6.033 (or equivalent); no prior database experience is assumed though students who have taken an undergraduate course in databases are encouraged to attend.
This module introduces estimation theory and its terminology, including bias, consistency, and efficiency. In searching for methods of extracting information from noisy observations, this chapter describes estimation theory, which has the goal of extracting from noise-corrupted observations the values of disturbance parameters (noise variance, for example), signal parameters (amplitude or propagation direction), or signal waveforms. Estimation theory assumes that the observations contain an information-bearing quantity, thereby tacitly assuming that detection-based preprocessing has been performed (in other words, do I have something in the observations worth estimating?). Conversely, detection theory often requires estimation of unknown parameters: Signal presence is assumed, parameter estimates are incorporated into the detection statistic, and consistency of observations and assumptions tested. Consequently, detection and estimation theory form a symbiotic relationship, each requiring the other to yield high-quality signal processing algorithms.
Subject:
Mathematics and Statistics, Science and Technology
The course focuses on the problem of supervised learning within the framework of Statistical Learning Theory. It starts with a review of classical statistical techniques, including Regularization Theory in RKHS for multivariate function approximation from sparse data. Next, VC theory is discussed in detail and used to justify classification and regression techniques such as Regularization Networks and Support Vector Machines. Selected topics such as boosting, feature selection and multiclass classification will complete the theory part of the course. During the course we will examine applications of several learning techniques in areas such as computer vision, computer graphics, database search and time-series analysis and prediction. We will briefly discuss implications of learning theories for how the brain may learn from experience, focusing on the neurobiology of object recognition. We plan to emphasize hands-on applications and exercises, paralleling the rapidly increasing practical uses of the techniques described in the subject.
" This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods."
The course introduces statistical theory to prepare students for the remainder of the econometrics sequence. The emphasis of the course is to understand the basic principles of statistical theory. A brief review of probability will be given; however, this material is assumed knowledge. The course also covers basic regression analysis. Topics covered include probability, random samples, asymptotic methods, point estimation, evaluation of estimators, Cramer-Rao theorem, hypothesis tests, Neyman Pearson lemma, Likelihood Ratio test, interval estimation, best linear predictor, best linear approximation, conditional expectation function, building functional forms, regression algebra, Gauss-Markov optimality, finite-sample inference, consistency, asymptotic normality, heteroscedasticity, and autocorrelation.
Mathematical models of systems from observations of their behavior. Time series, state-space, and input-output models. Model structures, parametrization, and identifiability. Non-parametric methods. Prediction error methods for parameter estimation, convergence, consistency, andasymptotic distribution. Relations to maximum likelihood estimation. Recursive estimation; relation to Kalman filters; structure determination; order estimation; Akaike criterion; and bounded but unknown noise models. Robustness and practical issues.
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