,concept,description,embedding,topic_0,topic_1,topic_2,topic_3,topic_4,topic_0_desc,topic_1_desc,topic_2_desc,topic_3_desc,topic_4_desc
0,Supervised Learning,"In supervised learning, the algorithm learns from labeled data, where each example is paired with a corresponding target label. 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labelstrainingdatatestexamplepredictedlabelflearningalgorithmFigure 11 The general supervised ap proach to machine learning a learning algorithm reads in training data and computes a learned function f  This function can then automatically label future text examplesWhy is it bad if the learning algo rithm gets to peek at the test data910 a course in machine learningated on the test data The machine learning algorithm has succeeded if its performance on the test data is high12 Some Canonical Learning Problems,So far we have largely considered machine learning problems in which the goal of the learning algorithm is to make a single prediction In many real world problems however an algo rithm must make a sequence of decisions with the world possibly changing during that sequence Such problems are often called se quential decision making problems A straightforward example which will be the running example for this chapteris that of self driving cars We want to train a machine learning algorithm to drive a car But driving a car is not a single prediction its a sequence of predictions,Up through this point you have learned all about supervised learn ing in particular binary classification As another example of the use of geometric intuitions and data we are going to temporarily consider an unsupervised learning problem In unsupervised learn ing our data consists only of examples xn and does not contain corre sponding labels Your job is to make sense of this data even though no one has provided you with correct labels The particular notion of making sense of that we will talk about now is the clustering task Consider the data shown in Figure 313 Since this,The general approach to machine learning which captures many ex isting learning algorithms is the modeling approach The idea is that we come up with some formal model of our data For instance we might model the classification decision of a studentcourse pair as a decision tree The choice of using a tree to represent this model is our choice We also could have used an arithmetic circuit or a polynomial or some other function The model tells us what sort of things we can learn and also tells us what our inductive bias is,This general set up of predicting the future based on the past is at the core of most machine learning The objects that our algorithm will make predictions about are examples In the recommender sys tem setting an example would be some particular StudentCourse pair such as AliceAlgorithms The desired prediction would be the rating that Alice would give to Algorithms,General approach to supervised machine learning algorithms.,Sequential decision making in supervised learning tasks.,Introduction to unsupervised learning and clustering task.,Modeling approach in supervised learning algorithms.,"Predicting future based on past, using examples for predictions."
1,Unsupervised Learning,"Unsupervised learning involves training algorithms on unlabeled data. 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without a teacher One basic thing that you might want to do with data is to visualize it Sadly it is difficult to visualize things in more than two or three dimensions and most data is in hundreds of dimensions or more Dimension ality reduction is the problem of taking high dimensional data and embedding it in a lower dimension space Another thing you might want to do is automatically derive a partitioning of the data into clusters Youve already learned a basic approach for doing this the kmeans algorithm Chapter 3 Here you will analyze this,Up through this point you have learned all about supervised learn ing in particular binary classification As another example of the use of geometric intuitions and data we are going to temporarily consider an unsupervised learning problem In unsupervised learn ing our data consists only of examples xn and does not contain corre sponding labels Your job is to make sense of this data even though no one has provided you with correct labels The particular notion of making sense of that we will talk about now is the clustering task Consider the data shown in Figure 313 Since this,decision treesknown labelstrainingdatatestexamplepredictedlabelflearningalgorithmFigure 11 The general supervised ap proach to machine learning a learning algorithm reads in training data and computes a learned function f  This function can then automatically label future text examplesWhy is it bad if the learning algo rithm gets to peek at the test data910 a course in machine learningated on the test data The machine learning algorithm has succeeded if its performance on the test data is high12 Some Canonical Learning Problems,Implement latent semantic analysis for text dataIf you have access to labeled training data you know what to do This is the supervised setting in which you have a teacher telling you the right answers Unfortunately finding such a teacher is often difficult expensive or down right impossible In those cases you might still want to be able to analyze your data even though you do not have labelsMotivate manifold learning from the perspective of reconstruction errorUnderstand Kmeans clustering as distance minimization,sional space we can start performing geometric operations on this data For instance suppose you need to predict whether Alice will like Algorithms Perhaps we can try to find another student who is most similar to Alice in terms of favorite courses Say this student is Jeremy If Jeremy liked Algorithms then we might guess that Alice will as well This is an example of a nearest neighbor model of learn ing By inspecting this model well see a completely different set of answers to the key learning questions we discovered in Chapter 1Dependencies Chapter 1,Dimensionality reduction and data clustering in unsupervised learning.,Unsupervised learning - clustering task without provided labels.,Supervised learning general approach and testing data peeking.,Unsupervised learning techniques and their advantages discussed.,Nearest neighbor model for predicting preferences and dependencies.
2,Regression Analysis,Regression analysis is a statistical method used to predict a continuous target variable based on one or more predictor variables. 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problems The primary difference between them is in what type of thing theyre trying to predict Here are some examplesRegression trying to predict a real value For instance predict thevalue of a stock tomorrow given its past performance Or predict Alices score on the machine learning final exam based on her homework scores,Starting with the case of regression is actually somewhat simpler than starting with classification in this case Suppose you believe that the relationship between the real value y and the vector x should be linear That is you expect that y  w  x  b should hold for some parameters w b Of course the data that you get does not exactly obey this thats fine you can think of deviations from y  w  x  b as noise To form a probabilistic model you must assume some distribution over noise a convenient choice is zeromean Gaussian noise This leads to the following generative story,It is often the case that instead of predicting a single output you need to predict multiple correlated outputs simultaneously In nat ural language processing you might want to assign a syntactic label like noun verb adjective etc to words in a sentence there is clear correlation among these labels In computer vision you might want to label regions in an image with object categories again there is correlation among these regions The branch of machine learning that studies such questions is structured prediction,At a basic level machine learning is about predicting the future based on the past For instance you might wish to predict how much a user Alice will like a movie that she hasnt seen based on her rat ings of movies that she has seen This prediction could be based on many factors of the movies their category drama documentary etc the language the director and actors the production company etc In general this means making informed guesses about some un observed property of some object based on observed properties of that object,In the preceeding chapters you have learned all about a very simple form of prediction predicting bits In the real world how ever we often need to predict much more complex objects You may need to categorize a document into one of several categories sports entertainment news politics etc You may need to rank web pages or ads based on relevance to a query These problems are all com monly encountered yet fundamentally more complex than binary classificationRecognize the difference between regression and ordinal regression,Examples of inductive learning problems predicting real values.,Intro to linear regression with Gaussian noise model.,Multi-output prediction in structured data with correlations.,Prediction of future based on past observations.,Text discusses complex prediction problems in regression analysis.
3,Classification Algorithms,"Classification algorithms are used to predict discrete class labels for new instances based on past observations. 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problems in which the goal of the learning algorithm is to make a single prediction In many real world problems however an algo rithm must make a sequence of decisions with the world possibly changing during that sequence Such problems are often called se quential decision making problems A straightforward example which will be the running example for this chapteris that of self driving cars We want to train a machine learning algorithm to drive a car But driving a car is not a single prediction its a sequence of predictions,Classify learning algorithms based on whether they are errordriven or notImplement the perceptron algorithm for binary classificationSo far youve seen two types of learning models in decision trees only a small number of features are used to make decisions in nearest neighbor algorithms all features are used equally Neither of these extremes is always desirable In some problems we might want to use most of the features but use some more than others,The general approach to machine learning which captures many ex isting learning algorithms is the modeling approach The idea is that we come up with some formal model of our data For instance we might model the classification decision of a studentcourse pair as a decision tree The choice of using a tree to represent this model is our choice We also could have used an arithmetic circuit or a polynomial or some other function The model tells us what sort of things we can learn and also tells us what our inductive bias is,Binary Classification trying to predict a simple yesno response For instance predict whether Alice will enjoy a course or not Or predict whether a user review of the newest Apple product is positive or negative about the productMulticlass Classification trying to put an example into one of a num ber of classes For instance predict whether a news story is about entertainment sports politics religion etc Or predict whether a CS course is Systems Theory AI or OtherRanking trying to put a set of objects in order of relevance For in,This general set up of predicting the future based on the past is at the core of most machine learning The objects that our algorithm will make predictions about are examples In the recommender sys tem setting an example would be some particular StudentCourse pair such as AliceAlgorithms The desired prediction would be the rating that Alice would give to Algorithms,Sequential decision making in machine learning classification algorithms.,Comparison of feature usage in learning algorithms.,Modeling approach for machine learning classification algorithms.,Classification Algorithms in different decision-making scenarios.,Predicting future based on past for classification algorithms.
4,Clustering Techniques,"Clustering techniques group similar data points together based on their characteristics. 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the bottom set of points C Or perhaps you permuted these labels But chances are your clusters were the same as mine The Kmeans clustering algorithm is a particularly simple and effective approach to producing clusters on data like you see in Fig ure 313 The idea is to represent each cluster by its cluster center Given cluster centers we can simply assign each point to its nearestgeometry and nearest neighborsFigure 311 decision tree for ski vs snowboard,assumes that nearby points should have the same label Another aspect which is quite different from decision trees is that all features are equally important Recall that for decision trees the key question was which features are most useful for classification The whole learning algorithm for a decision tree hinged on finding a small set of good features This is all thrown away in KNN classifiers every feature is used and they are all used the same amount This means that if you have data with only a few relevant features and lots of irrelevant features KNN is likely to do poorly,Unsupervised learning is learning without a teacher One basic thing that you might want to do with data is to visualize it Sadly it is difficult to visualize things in more than two or three dimensions and most data is in hundreds of dimensions or more Dimension ality reduction is the problem of taking high dimensional data and embedding it in a lower dimension space Another thing you might want to do is automatically derive a partitioning of the data into clusters Youve already learned a basic approach for doing this the kmeans algorithm Chapter 3 Here you will analyze this,Up through this point you have learned all about supervised learn ing in particular binary classification As another example of the use of geometric intuitions and data we are going to temporarily consider an unsupervised learning problem In unsupervised learn ing our data consists only of examples xn and does not contain corre sponding labels Your job is to make sense of this data even though no one has provided you with correct labels The particular notion of making sense of that we will talk about now is the clustering task Consider the data shown in Figure 313 Since this,Suppose that you dont have labels Analogously to the Kmeans algorithm one potential solution is to iterate You can start off with guesses for the values of the unknown variables and then iteratively improve them over time In Kmeans the approach was the assign examples to labels or clusters This time instead of making hard assignments example 10 belongs to cluster 4 well make soft as signments example 10 belongs half to cluster 4 a quarter to cluster 2 and a quarter to cluster 5 So as not to confuse ourselves too much well introduce a new variable zn ,Introduction to K-means clustering algorithm for data analysis.,Equal weighting of all features in KNN classification.,Introduction to unsupervised learning and dimensionality reduction techniques.,Introduction to unsupervised clustering with geometric intuitions.,Soft assignment in clustering with iterative improvement approach.
5,Dimensionality Reduction,Dimensionality reduction techniques aim to reduce the number of features in a dataset while preserving its essential information. 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taking a dataset in high di mensions say 10000 and reducing it to low dimensions say 2 while retaining the important characteristics of the data Since this is an unsupervised setting the notion of important characteristics is difficult to defineConsider the dataset in Figure 151 which lives in high dimensions,two and you want to reduce to low dimensions one In the case of linear dimensionality reduction the only thing you can do is to project the data onto a vector and use the projected distances as the embeddings Figure 152 shows a projection of this data onto the vector that points in the direction of maximal variance of the original dataset Intuitively this is a reasonable notion of importance since this is the direction in which most information is encoded in the data,ality reduction as in clustering If the purpose of dimensionality reduction is to visualize then K should be 2 or 3 However an alter native purpose of dimensionality reduction is to avoid the curse of dimensionality For instance even if you have labeled data it might be worthwhile to reduce the dimensionality before applying super vised learning essentially as a form of regularization In this case the question of an optimal K comes up again In this case the same criteria AIC and BIC that can be used for clustering can be used for PCA The only difference is the quality measure,Unsupervised learning is learning without a teacher One basic thing that you might want to do with data is to visualize it Sadly it is difficult to visualize things in more than two or three dimensions and most data is in hundreds of dimensions or more Dimension ality reduction is the problem of taking high dimensional data and embedding it in a lower dimension space Another thing you might want to do is automatically derive a partitioning of the data into clusters Youve already learned a basic approach for doing this the kmeans algorithm Chapter 3 Here you will analyze this,This leads to the technique of principle components analysis or PCA For completeness the is depicted in Algorithm 152 The important thing to note is that the eigenanalysis only gives you the projection directions It does not give you the embedded data To embed a data point x you need to compute its embedding as cid104x  u1 x  u2     x  uKcid105 If you write U for the DK matrix of us then this is just XUThere is an alternative derivation of PCA that can be informative,Reducing high-dimensional data to retain important characteristics.,Projection of data onto vector for dimensionality reduction.,Optimal K selection in Dimensionality Reduction techniques.,Reducing high dimensional data to lower dimensions.,PCA algorithm for embedding data in lower dimensions.
6,Model Evaluation and Selection,"Model evaluation involves assessing the performance of machine learning models using metrics like accuracy, precision, recall, and F1-score. 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but not othersExplain the relationship between the three learning techniques you have seen so farApply several debugging techniques to learning algorithmsIn many ways going from an abstract problem to a concrete learn,The reason that it is convenient to break machine learning prob lems down by the type of object that theyre trying to predict has to do with measuring error Recall that our goal is to build a system that can make good predictions This begs the question what does it mean for a prediction to be good The different types of learning problems differ in how they define goodness For instance in regres sion predicting a stock price that is off by 005 is perhaps much better than being off by 20000 The same does not hold of multi class classification There accidentally predicting,The main message for evaluation metrics is that you should choosewhichever one makes the most sense In many cases several might make sense In that case you should do whatever is more commonly done in your field There is no reason to be an outlier without cause56 Cross ValidationIn Chapter 1 you learned about using development data or heldout data to set hyperparameters The main disadvantage to the develop ment data approach is that you throw out some of your training data just for estimating one or two hyperparametersAlgorithm 8 CrossValidateLearningAlgorithm Data K,training datab Compute this models error rate on the development data3 From the above collection of models choose the one that achievedthe lowest error rate on development data4 Evaluate that model on the test data to estimate future test performance27 Real World Applications of Machine Learning,The general approach to machine learning which captures many ex isting learning algorithms is the modeling approach The idea is that we come up with some formal model of our data For instance we might model the classification decision of a studentcourse pair as a decision tree The choice of using a tree to represent this model is our choice We also could have used an arithmetic circuit or a polynomial or some other function The model tells us what sort of things we can learn and also tells us what our inductive bias is,Summary of various evaluation metrics and techniques.,Measuring error and defining goodness in different learning problems.,"Choose appropriate evaluation metric, avoid unnecessary data loss.",Evaluation of model performance and selection process.,The importance of modeling in machine learning algorithms.
7,Overfitting and Regularization,"Overfitting occurs when a model learns to capture noise in the training data rather than underlying patterns, leading to poor generalization performance on unseen data. 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illustrates the key concepts of underfitting and overfitting Underfitting is when you had the opportunity to learn something but didnt A student who hasnt studied much for an up coming exam will be underfit to the exam and consequently will not do well This is also what the empty tree does Overfitting is when you pay too much attention to idiosyncracies of the training data and arent able to generalize well Often this means that your model is fitting noise rather than whatever it is supposed to fit A student who memorizes answers to past exam questions without understand,Since bagging tends to reduce variance it provides an alternative approach to regularization That is even if each of the learned clas sifiers f1     f M are individually overfit they are likely to be overfit to different things Through voting you are able to overcome a sig nificant portion of this overfitting Figure 132 shows this effect by comparing regularization via hyperparameters to regularization via bagging132 Boosting Weak Learners,the number of passes to make over the training data If we make many many passes over the training data then the algorithm is likely to overfit This would be like studying too long for an exam and just confusing yourself On the other hand going over the data only one time might lead to underfitting This is shown experimentally in Figure 43 The xaxis shows the number of passes over the data and the yaxis shows the training error and the test error As you can see there is a sweet spot at which test performance begins to degrade due to overfitting,For now we will ignore the idea of regularization This is for two reasons The first is that you already know how to deal with regular ization so everything youve learned before applies The second is that historically neural networks have not been regularized Instead people have used early stopping as a method for controlling overfit ting Presently its not obvious which is a better solution both are104valid optionsTo be completely explicit we will focus on optimizing squared,training data and a regularizer how complicated is our learned model This learning framework is known as both Tikhonov regularization and structural risk mini mization,Underfitting and overfitting in machine learning models.,Regularization through bagging reduces overfitting in classifiers.,Importance of determining optimal number of training passes.,"Neural networks historically not regularized, using early stopping.",Regularization balances complexity and training data to prevent overfitting.
8,Feature Engineering in Machine Learning,"Feature engineering involves creating new features or transforming existing ones to improve the performance of machine learning models. 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think about an example as being represented by a feature vector consisting of one dimension for each feature where each dimenion is simply some real valueConsider a review that said excellent three times had one excla30 a course in machine learning,31 From Data to Feature VectorsAn example is just a collection of feature values about that example for instance the data in Table 1 from the Appendix To a person these features have meaning One feature might count how many times the reviewer wrote excellent in a course review Another might count the number of exclamation points A third might tell us if any text is underlined in the review,You can think of prediction tasks as mapping inputs course reviews to outputs course ratings As you learned in the previ ous chapter decomposing an input into a collection of features eg words that occur in the review forms a useful abstraction for learn ing Therefore inputs are nothing more than lists of feature values This suggests a geometric view of data where we have one dimen sion for every feature In this view examples are points in a high dimensional spaceDraw decision boundariesImplement the Kmeans algorithm for clustering,148efficient learning 175176 a course in machine learning144 Feature HashingAs much as speed is a bottleneck in prediction so often is memory usage If you have a very large number of features the amount of memory that it takes to store weights for all of them can become prohibitive especially if you wish to run your algorithm on small de vices Feature hashing is an incredibly simple technique for reducing the memory footprint of linear models with very small sacrifices in accuracy,ing task is more of an art than a science However this art can have a huge impact on the practical performance of learning systems In many cases moving to a more complicated learning algorithm will gain you a few percent improvement Going to a better representa tion will gain you an order of magnitude improvement To this end we will discuss several high level ideas to help you develop a better artistic sensibilityDependencies Chapter 1Chap ter 3Chapter 451 The Importance of Good Features,Text describes feature representation in machine learning tasks.,Extracting meaningful attributes from data for ML models.,Geometric view of data and feature abstraction.,Reduce memory usage for large number of features.,Feature engineering is an art with huge impact.
9,Neural Networks and Deep Learning,"Neural networks are a class of machine learning models inspired by the structure and function of the human brain. Deep learning refers to neural networks with multiple hidden layers, capable of learning complex representations from data. They have achieved state-of-the-art performance in various tasks like image recognition, natural language processing, and speech recognition.","[-0.030481623485684395, 0.013014698401093483, 0.015744106844067574, -0.011950034648180008, 0.012130704708397388, -0.00562658254057169, 0.010040094144642353, 0.009781993925571442, -0.013859976083040237, -0.02741023153066635, -0.009575514122843742, 0.039824847131967545, -0.025384144857525826, 0.002056735334917903, -0.005042630713433027, 0.026235876604914665, 0.0345337949693203, -0.0011985524324700236, 0.004290914162993431, -0.01903488300740719, -0.032185085117816925, 0.008833476342260838, -0.005739501211792231, -0.04036685824394226, -0.009388391859829426, -0.00019176032219547778, 0.016673266887664795, -0.02888140268623829, -0.0003671877202577889, -0.019770467653870583, 0.02746185101568699, -0.007149373181164265, 0.005120060872286558, -0.0009420653805136681, 0.015460196882486343, -0.005278147291392088, 0.005203943233937025, -0.018286392092704773, 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the major weaknesses of linear models like perceptron and the regularized linear models from the previous chapter is that they are linear Namely they are unable to learn arbitrary decision bound aries In contrast decision trees and KNN could learn arbitrarily complicated decision boundaries,The first learning models you learned about decision trees and nearest neighbor models created complex nonlinear decision boundaries We moved from there to the perceptron perhaps the most classic linear model At this point we will move back to non linear learning models but using all that we have learned about linear learning thus farExplain the tradeoff between depth and breadth in network structureContrast neural networks with ra dial basis functions with knearest neighbor learning,The definition of neural networks and the backpropagation algo rithm can be generalized beyond two layers to any arbitrary directed acyclic graph In practice it is most common to use a layered net work like that shown in Figure 104 unless one has a very strong reason aka inductive bias to do something different However the view as a directed graph sheds a different sort of insight on the back propagation algorithm,This chapter presents an extension of perceptron learning to non linear decision boundaries taking the biological inspiration of neu rons even further In the perceptron we thought of the input data point eg an image as being directly connected to an output eg label This is often called a singlelayer network because there is one layer of weights Now instead of directly connecting the inputs to the outputs we will insert a layer of hidden nodes moving from a singlelayer network to a multilayer network But introducing a nonlinearity at inner layers this will give us,Another difficulty of neural networks is that their weights can be difficult to interpret Youve seen that for linear networks you can often interpret high weights as indicative of positive examples and low weights as indicative of negative examples In multilayer networks it becomes very difficult to try to understand what the different hidden units are doing104 Beyond Two Layers,Limitations of linear models in learning complex boundaries.,Comparison of linear and non-linear learning models.,Generalization of neural networks beyond two layers.,Extension of perceptron learning to non linear networks.,Challenges of interpreting weights in multilayer neural networks.
10,Optimization Methods in Machine Learning,"Optimization methods are used to train machine learning models by adjusting their parameters to minimize a loss function. Gradient descent is a commonly used optimization algorithm, with variations like stochastic gradient descent and mini-batch gradient descent.","[-0.02417256496846676, 0.0036600667517632246, 0.025888120755553246, -0.012421654537320137, -0.0004024864174425602, 0.02685553953051567, 0.02441764436662197, 0.007100852206349373, -0.00847458653151989, -0.04303077608346939, 0.006771930027753115, 0.042540617287158966, -0.009738679975271225, 0.0030006098095327616, -0.006307568866759539, 0.0020057810470461845, 0.032402072101831436, 0.015323909930884838, 0.015233617275953293, 0.007668404374271631, -0.039444878697395325, 0.01381473708897829, 0.0066235922276973724, -0.03077680803835392, -0.011950843967497349, 0.0071782455779612064, 0.02022549696266651, -0.029177343472838402, 0.026442773640155792, -0.004524294286966324, 0.019554752856492996, 0.007004110142588615, -0.00019811926176771522, -0.016394520178437233, -0.016794385388493538, -0.001821971614845097, 0.019580552354454994, 0.006007669027894735, 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generic optimization algorithm there are cases when you can do better An example is the case of a 2norm regularizer and squared error loss function For this you can actually obtain a closed form solution for the optimal weights How ever to obtain this you need to rewrite the optimization problem in terms of matrix operations For simplicity we will only consider thelinear models9798 a course in machine learning,The idea of gradientbased methods of optimization is exactly thesame Suppose you are trying to find the maximum of a function f x The optimizer maintains a current estimate of the parameter of interest x At each step it measures the gradient of the function it is trying to optimize This measurement occurs at the current location x Call the gradient g It then takes a step in the direction of the gradient where the size of the step is controlled by a parameter η eta The complete step is x  x  ηg This is the basic idea of gradient ascent,In DecisionTreeTrain as in most machine learning the learning algorithm is essentially trying to adjust the parameters of the model so as to minimize training error This suggests an idea for choosing hyperparameters choose them so that they minimize train ing error,means is it optimizing what you think its optimizing Instead of measuring accuracy try measuring whateverquantityyour algorithmissupposedlyoptimizing like log loss or hinge loss and make sure that the optimizer is successfully minimizing this quantity It is usually useful to handcraft some datasets on which you know the desired behavior For instance you could run KNN on the XOR data Or you could run perceptron on some easily linearly separa ble data for instance positive points along the line x2  x1  1 and negative points along the line x2  x1  1 Or a decision tree on,learning problems will be framed as minimization problems trying to reach the bottom of a ditch rather than the top of a hill There fore descent is the primary approach you will use One of the major conditions for gradient ascent being able to find the true global min imum of its objective function is convexity Without convexity all is lost,Closed form solution for optimal weights in linear models.,Gradient ascent for finding maximum in optimization methods.,Optimizing hyperparameters to minimize training error.,Testing and optimizing algorithms on handcrafted datasets.,Emphasizing descent for optimal solutions in machine learning.
11,Bias-Variance Tradeoff,"The bias-variance tradeoff refers to the dilemma in machine learning between bias and variance. A model with high bias underfits the training data, while a model with high variance overfits the training data. Achieving an optimal balance between bias and variance is crucial for building models that generalize well to unseen data.","[-0.030276184901595116, -0.012224373407661915, 0.0342494361102581, -0.011423100717365742, -0.012489257380366325, 0.01836967095732689, -0.007959749549627304, 0.01415802352130413, -0.022568074986338615, -0.06113511323928833, 0.01934974081814289, 0.033295854926109314, -0.010721160098910332, -0.020541716367006302, -0.0023392525035887957, 0.0014676201390102506, 0.03610362112522125, 0.0029650398064404726, 0.010184770449995995, -0.038567036390304565, -0.037904828786849976, 0.020210610702633858, -0.034938134253025055, -0.024859316647052765, -0.024766607210040092, 0.017614753916859627, 0.021455563604831696, -0.011244304478168488, 0.00589365791529417, 0.005575797986239195, 0.013283907435834408, 0.015045383013784885, -0.02083308808505535, -0.006267806049436331, -0.008946440182626247, -0.011502565816044807, 0.0035461278166621923, 0.008310720324516296, 0.039017338305711746, 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approximation error is bias and estimation error is variance To understand this connection consider a very simple hypothesis class F that only contains two functions the always positive classifier that returns 1 regardless of input and the always negative classifier Suppose you have a data generating distribution D that is 60 positive examples and 40 negative examples You draw a training set of 41 exam ples Theres about a 90 chance that the majority of these training examples will be positive so on this impoverished,This is clearly undesirable behavior especially since data is expen sive in a machine learning setting One solution there are others is to seek parameters that balance a tradeoff between the likelihood of the data and some prior belief you have about what values of those parameters are likely Taking the case of the logistic regression you might a priori believe that small values of w are more likely than large values and choose to represent this as a Gaussian prior on each component of w,Do you have enough data Try training on 80 of your training data and look at how much this hurts performance If it hurts a lot then getting more data is likely to help if it only hurts a little you might be data saturated59 BiasVariance TradeoffBecause one of the key questions in machine learning is the question of representation it is common to think about test error in terms of a decomposition into two terms Let f be the learned classifier selected from a set F of all possible classifiers using a fixed representation thenerror f  cid20cid124error f ,At the end of Chapter 1 you saw the Russian Tank example of a biased data set leading to a classifier that seemed like it was doing well but was really relying on some artifact of the data collection process As machine learning algorithms have a greater and greater impact on the real world it is crucially important to ensure that they are making decisions based on the right aspects of the input rather than exploiting arbitrary idiosyncracies of a particular training set For the rest of this chapter we will consider two real world ex amples of bias issues that have had significant,Throughout this book you will learn about several approaches to machine learning The decision tree model is the first such approach These approaches differ primarily in the sort of inductive bias thatclassBclass AFigure 21 Training data for a binary classification problemFigure 22 Test data for the same classification problemIt is also possible that the correct classification on the test data is ABAB This corresponds to the bias is the background in focus Some how no one seems to come up with this classification rulethey exhibit,Simple example illustrating bias-variance tradeoff concept.,Balancing data likelihood and prior belief for parameters.,Consider data size impact on model performance.,Real-world examples highlighting importance of avoiding bias.,Inductive bias and background focus in classification rules.