More...In more detail, it turns out that even when the optimal parameter vector we're searching for lives in a very high-dimensional vector space (dimension being the number of features), a basic linear algebra argument shows that for certain objective functions, the optimal parameter vector lives in a subspace spanned by the training input vectors.

So far we have studied the regression setting, for which our predictions (i.e. 33 0 obj

We compare the two approaches for the simple problem of learning about a coin's probability of heads. When using linear hypothesis spaces, one needs to encode explicitly any nonlinear dependencies on the input as features. Given this model, we can then determine, in real-time, how "unusual" the amount of behavior is at various parts of the city, and thereby help you find the secret parties, which is of course the ultimate goal of machine learning. types of features?

weak-learning, strong-learning, and adaboost, Streaming Algorithms: More...Although it's hard to find crisp theoretical results describing when bagging helps, conventional wisdom says that it helps most for models that are "high variance", which in this context means the prediction function may change a lot when you train with a new random sample from the same distribution, and "low bias", which basically means fitting the training data well. Solutions (for instructors only): follow the link and click on "Instructor Resources" to request access to the solutions. The primary goal of the class is to help participants gain a deep understanding of the concepts, techniques and mathematical frameworks used by experts in machine learning. Sometimes the dot product between two feature vectors f(x) and f(x') can be computed much more efficiently than multiplying together corresponding features and summing. We motivate bagging as follows: Consider the regression case, and suppose we could create a bunch of prediction functions, say B of them, based on B independent training samples of size n. If we average together these prediction functions, the expected value of the average is the same as any one of the functions, but the variance would have decreased by a factor of 1/B -- a clear win! leverage multiple related learning tasks, or leverage multiple

Machine learning algorithms essentially search through all the possible patterns that exist between a set of descriptive features and a target feature to ﬁnd the best model that is This is where gradient boosting is really needed.

More...Notably absent from the lecture is the hard-margin SVM and its standard geometric derivation. The quickest way to see if the mathematics level of the course is for you is to take a look at this mathematics assessment, which is a preview of some of the math concepts that show up in the first part of the course. What does this mean?

If you're already familiar with standard machine learning practice, you can skip this lecture. Introduction to Statistical Learning Theory, Directional Derivatives and Approximation (Short), Zou and Hastie's Elastic Net Paper (2005), Mairal, Bach, and Ponce on Sparse Modeling, 8. We introduce "regularization", our main defense against overfitting.

To this end, we introduce "subgradient descent", and we show the surprising result that, even though the objective value may not decrease with each step, every step brings us closer to the minimizer. More...If the base hypothesis space H has a nice parameterization (say differentiable, in a certain sense), then we may be able to use standard gradient-based optimization methods directly. Course description: This course will cover fundamental Computation Graphs, Backpropagation, and Neural Networks. x��S�n�0ݽ�4��Y��9�@� ��?\$i�"Gst��W�e'F �"2��2����C�ű���ry�n�K�P Finally, we present "coordinate descent", our second major approach to optimization. We introduce the basics of convex optimization and Lagrangian duality. With the abundance of well-documented machine learning (ML) libraries, programmers can now "do" some ML, without any understanding of how things are working.

Large decision trees have these characteristics and are usually the model of choice for bagging. (Credit to Brett Bernstein for the excellent graphics.).

We will also examine other important constraints and stream Backpropagation for the multilayer perceptron, the standard introductory example, is presented in detail in Hwk 7 Problem 4. hypotheses, VC-dimension, and Sauer's lemma, Sample complexity results When L1 and L2 regularization are applied to linear least squares, we get "lasso" and "ridge" regression, respectively.

With linear methods, we may need a whole lot of features to get a hypothesis space that's expressive enough to fit our data -- there can be orders of magnitude more features than training examples. For classical "frequentist" statistics, we define statistics and point estimators, and discuss various desirable properties of point estimators. In fact, neural networks may be considered in this category. Regression trees are the most commonly used base hypothesis space. topics in Machine Learning and Data Science, including powerful For practical applications, it would be worth checking out the GBRT implementations in XGBoost and LightGBM. We start by discussing various models that you should almost always build for your data, to use as baselines and performance sanity checks. After reparameterization, we'll find that the objective function depends on the data only through the Gram matrix, or "kernel matrix", which contains the dot products between all pairs of training feature vectors. 298

optimization III: FTRL contd, and Follow the Perturbed Leader, Boosting: to Statistical Learning Theory, Theory of Disagreement-Based Active Learning, Active Learning of Linear KDD Cup 2009: Customer relationship prediction, 3. To make proper use of ML libraries, you need to be conversant in the basic vocabulary, concepts, and workflows that underlie ML.

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and making sense of massive datasets, especially under limited The algorithm we present applies, without change, to models with "parameter tying", which include convolutional networks and recurrent neural networks (RNN's), the workhorses of modern computer vision and natural language processing.