Datasets:

Meyerger

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ASAG2024

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1. Weigths in the network 2. the center of the clusters 3. variation of the cluster ($\sigma$) Difference: RBF always have only three layers RBF can also trained in an unspervised method RBF can also approximate any continuous function

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

- The centroids of the radial basis functions - The weights of the neurons - The amount of needed neurons A difference to other neural networks is that the centroids of the radial basis functions need to be there.

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

The centers of the clusters, the widhts of the clusters and the weights. In contrast to other NNs the output only depends on the radial distance to the center of the clusters.

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

The weights, the interpolation matrix have to be learned. The RBF maps the input space into a higher dimensional feature space nonlinearly. The feature space is mapped into the output space linearly. The output space is much smaller than the feature space. Pros: local learning Cons: feature space can be really large, curse of dimensionality

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

The clusters, the width of the basis function and the weights. The clusters and the width are learned in an unsupervised fashion. While the weights are learning by a standard supervised steepest descent method. Pros RBFs can be very easily trained. RBFs can achieve better results with less complexity. Cons Not as easy to understand

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

Centers of the radial basis functions best model (rbf) distance of each input pair pros: non-linear functions application ease to compute using covers theorem cons: high-dimensional

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

Centroids, width, and parameter of function The learning of an rbfn is splitted in an unsupervised and a supervised part. Only one layer, no vanishing gradient. Pros: easy learning the unsupervised part is not very sensitive. Cons: Difficult to approximate constants

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

1. Input layer connecting RBF to environment. 2. Hidden layer: nonolinear tranformation of input space to hidden space 3. Output layer: linear tranformation of hidden space to output space. It is different than other NNs because for learning patterns, it nonlinearly tranforms the input space to higher dimmensional space. Other NNs do not tranform input. As it tranforms input patterns to high dimmensional nonlinear space, patterns which are not separable in lower dimmensions have greater chance to be separated. But if we select basis functions equal to datapoints, problem is ill-formulated. Processing is computationallly heavy. Regualation becomes problem specific. Hence, unsupervied learning is employed to clusters data initially.

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

data varaince Features RBF uses suport vector machine which is classifier. it uses different kernels , it doesnot have feedback cycle. it also classifies non linear classification problem. it mainly works with 2 classes C1 ,C2. other NN is can also reggression and there can be feedback (RNN)

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

The difference of RBF to other NNS are 1. RBF has only one hidden layer wheras their is no hard limitation on number of hidden layers on other NNs 2. The activation function used in RBF is non linear.

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

A RBF network learns, * The radial function * weight of the hidden to output neuron * Centroid of a cluster Difference: * A RBF is composed of input layer, 1 hidden layer and the output layer. Other NN can generally use as many hidden layers as required. * The transformation from input to hidden layer in RBF is non linear and hidden to output is linear. In most other NN both are non linear. Pros/Cons: * This is a very simple learner * There are many variations of RBF available.

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

Three items to be learned are centers, weights, and biases. RBFN consists of a single hidden layer and a linear output layer. NN can have multiple hidden layers and a linear or non-linear output layer. Pros: RBFN is a universal approximator and it is easy to add more centers. Con: The bias is not unique.

DigiKlausur

K-nearest neighbors: 1. Take the input data to be classified. 2. Find the first nearest neighbour in terms of euclidean distance. 3. Push the class of this nearest neighbour into a list of labels. 4. Repeat step 2 and 3 for each K which needs to be odd. 5. After all K nearest labels are collected in the list, count the labels in each class. 6. Assign to the input data, the class which as maximum count (majority vote).

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

i. First we initialize the random points, those points are considered as centroids of clusters ii. Then, for each new points, we compute euclidean distance, and points closest to centrodis are assigned their respective clusters iii. We again re-calculate the centroids of clusters iv. Repeat 2 and 3 untill convergence is achieved, by making sure, no centroids are moving and cost function is minmized

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

k-nearest neighbor wants to determine encoder $\C which assigns N inputs to K clusters based on a rule to be defined.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

1. get the input 2. find the k- nearest neighbours by finding the distance (euclidean) from the input to all the nodes and selecting the k closest ones 3. Class of the input is the most frequent class in the k-neighbnours found (as such, k needs to be odd number)

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

$N$ number of clusters. Given sample data select $N$ different cluster centers by random. Assign all sample points to the closest cluster repeat until no further change: - recalucate the cluster centers - Assign all sample points to the closest cluster

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

given a fixed $k$ given a point to classify $new$ given an empty $class$ given a List of all points $L$ from 1 to k do find nearest point $x$ to $new$ in $L$ add class of neares point $x$ in list $class$ new list L = L without nearest neighboor $x$ class of new = most class in $class$

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Define K centroids, random intialised assign each data point a class label while the is no change anymore for each k calculate the centroid of the datapoint beloging to that label for each datapoint determine the nearest centroid assign a new class label which belongs to the centroid.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

K-nearest neighbors can be seen as an unsupervised learning method, where for a defined number of groups k, the nearest neighbors will be calculated. 1: For a given input data 2: Define value k 3: Get the k points that are closer to the given points.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

1- randomly define a predefined number of cluster centers(CC) 2- calculate the distance of each datapoint from each CC 3- Each data point belongs to the cluster that has the least distance from its CC 4- Calculate a new CC by getting the average of all the points inside a cluster 5- Go to 2 and repeat this process untill we reach the termination condition

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Firstly identify nearest neighbouring weights then choose k amount of neighbors and adapt their weights

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Initialize kneighbors = {}, for every neuron find the nearest neighbor and add it to kneighbors Return nearest kneighbors

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

** Pseudo Code ** 1. Initiate weights randomly 2. Assign labels to k-inputs that are map neuron is closest to. 3. append all inputs to map neurons using 2. 4. Find centroid of the cluster and move the map neuron to the centroid. 5. Do 2, and 4 until some convergence criteria is reached, e.g. maximum iterations is reached or no updates are performed or net distance is below some specified distance.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Given: L; XTEST not element of L; k = number of neighbors that will taken into consideration; function classof() Set x'={}, L0=L, Classf={}; for j=1,...k do: L{j-1} \ x'; //exclude all the data points which have been identified as nearest neighbors already x'=find the closest neighbor of XTEST in Lj; //e.g. compute eucldea distance c = classof(x'); Classf=push(c) set c(xTEST)= most frequently value in Classf;

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Train the knn by storing the data labeled points. Present a test point. > Compute the distance between the test point and all the training data points. > Sort the distance, and choose the k datapoints with smallest distance. > Determine the class of the test point by majority vote.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

L1 - Data set (x1,x2,x3,xn) L2 - Storing the dataset based on the number of neighbors. xtest - Test data set. So we basically have the k value to be an odd number, so that we can select a majority value. for i based on the number of l: x' = xtest - distance from the neighboring neuron i. L2 = smallest x' in this based on the number of K xtest = max(L2) We select the neurons from the neighborhood by calculating the euclidean distance based on weights. Then if K is 3, we have 3 neurons. So from that we select the label which is fixed maximum on the dataset given in the K-fields.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

define criterial for finding k nearest neighbours <br> find k nearest neigbours of test input in training dataset <br> find the class to which most of the neghbours belong <br> assign that class to the test input <br>

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

HERE: Learning based on K-nearest neighbors: - All the input-output samples from the training set are stored in the memory. - For a test input, find the k-nearest neighbors. - Assign the test vector with the class of the most of the neighbours in the neighborhood.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Parameters: k -number of clusters, x datapoints , c classes 1) Initialize randomly k centroid of the custers 2) select a data point and compute the set of nearest neighbours of the point using euclidean distances. 3) Find the class that maximum number of neighbours belong to and assign the class to the datapoint. 4) Once the class is assigned, compute the centroid of each cluster or class, considering all the class members. 5) Iterate over all the datapoints and repeat over all points (from step 2) until no update in centroids is required.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

1. Given: Classified data $X$ 2. For a new sample $x$: Determine the $k$ nearest neighbours in X Output $y$ := majority vote of the class of nearest neighbours

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

$ L = {x1,x2...xn} $ $L = L0$ $x' = {}$ for the input (x,d) : do { xtest }

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

1. identify k classified patterns that lie nearest to the test vector 2. assign the test vector to the class that is most frequently presented to the k nearest neighbors

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

1. Define the number of cluster (K) 2. Generate random weights 3. Find the center of each k (mean) 4. Cluster the other outputs by determining the closest neighbor 5. Update the weights

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

* Choose a value for k * K represents the number of neighbors * Get a sample from the input space * Find the class based on the majority of votes received from the neighbors. * For example, if the value of k is 3, then let say there are 2 neighbors from class one and 1 neighbor from class two, then the new input sample belongs to class one.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Step1: We randomly place the n neurons. Step2: For each data point whichever neuron is closer to it, the datapoint is assigned to that neuron. Step3: Once all the datapoints are assigned, the mean of the datapoints attached to each neuron is calculated and the neuron is shifted to the mean value. Step4: Step 2 and 3 are done until there is no more shift in the neurons position. In this way the neurons are adjusted.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Step1 : Randomly select the k centers Step2 : Cluster the datapoints based on the centers Step3 : the centroid of the cluster becomes the new mean Step4 : repeat step 2 and 3 until there is no more evidential cahnge in the network

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

input: labeled data set, one unlabeled data point, number k find the k labeled points, which are closest to the given unlabeled point from these points, find the label which occurs most often assign this label to the unlabeled data point

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

1. Get the nearest neighbor of the current x' 2. Remove it from L 3. Get the class of the current x 4. Classify x' as the class that occurs the most often in the neighbors for 1 to K: Li = L/x' xnn = min(|x-x'|) c = getclassof(xnn) AmountofClasses.add(c) setclassof(x') = Max(AmountofClasses)

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

For the input data x the distance to every other data point is calculated using a distance measure. Take the k data points, which have the minimum distance to x. These are the k-nearest neighbours. The most frequent class from the neighbours is assigned as the class of the input data.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

This learning is based on the memory introduced into the dataset. For each data point the nearest neighbours are found via a distance function. for each datapoint d neighbours = getknearestneighboursof(d) d.class = getmostrepresentedclass(neighbours)

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

for a given input compute distances to other input points pick k nearest neighboors look at labeling of neighboors decide labeling (classification) by highest number of neighboors in one class (german: Mehrheitsentscheid)

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

trainingset := training data define #clusters select #clusters datapoints as centroids randomly for datapoint in trainingset: calculate distance to centroid lable dataPoint according to closest centroid end for iterate over clusters: calculate centroid

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

(K-nearest neighbours is memory based learning.) take input x calculate calculate distance of x from each training point. Select K training points with minimum distce from the data. Fetch classes of selected K nearest points. Calculate number points per class in k nearest points. determine the class C having maximum points in k nearest pioints The class of the input point is C.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

K-nearest neighbors basically works as follows 1) the they define randomly the cluster points . 2) clacluate the mean of the equlidian distance between the data points. here the points from the previous step acts as centrioids. 3) check the variance of the clusters. 4) repeat 1-2-3 till you get the proper clusters.

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

1. Slect random number of neghbourhood initially 2. Find out the input which is nearest to the weight vector using competitive learning 3. Change only the input which wins 4. decrease the size of neighbourhood 5. Repeat

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

for x in inputpoints neighbours = findnearestkpoints(x) for n in neighbours v = getvoteof(n) updatevotescountfor(x,v) max = getmaxvotefor(x)

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

Let L be set of labeled data in memory, L ={x1,x2....xn}, while xprime is nearest point to the xtest point, in term of euclidean distance. Let classof be funtion that return class type if certain data point x. And let K be constant number of neighboring points consired in algorithm search. Initialize xprime = {}, L0 = L, listofclasses = {} for j= 1; j<=K; j++ do: Lj = L(j-1)/xprime xprime = nearest neighbor to Xtest form Lj data c = classof(xprime) listofclasses.append(c) end c(xtest):= most frequent class in listofclasses

Add the new data to the members of colored or classified old data, construct a sphere with k nearest data points, find the class or color which has the maximum vote and assign the new data to the class which has the maximum vote in an unsupervised manner.

DigiKlausur

In machine learning, a choice always needs to be made for the tradeoff between bias and variance. Bias determines how close the result is to the true value and variance determines the sensitivity to flutuations in the training dataset. If bias is reduced variance increases and vice versa. So an optimum tradeoff needs to be chosen which presents a dilemma.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias Variance dilemma is used to analyse the generalization error of the algorithm. If the value of Bias is very high, then network does not learn relations between features and outputs correctly(overfitting) If the value of variance is very high, then network may model the random noise, and it does not learn intended ouputs(underfitting) We have to to tradeoff between Bias and Variance so that our model can generalize properly

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

When training a model on a limited training data set, we must decide wether we accept a biased model which makes assumptions about the test data, but has a better performance on the train data, or a model with more variance which might model the entirety of the data better but be prone to data noise. Usually we have to decide on a trade off between the two, where we may select well balanced models based on VC dimensions or Cross validation results.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias and variance are both undesirable to the learning. Bias defines how far the generated output differs from the true value. Variance defines how much the o/p change on changing the input dataset. However, in most cases, it is only possible to decrease one at the expesne of other. Thus, it is called Bias Variance Dilemma.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

The bias is the error we make in the assumption by creating the learning machine (how much we we are away from the actual truth) the variance is how much the learning machine changes with different training data sets. if we have a high bias we habe a low variance and if we habe a low variance we habe a high bias

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

You have to to a tradeoff between high bias or high variance. You cannot have both. High vaiance means the model is overfitting the data and therefore the variance on input can be quit hight. High bias means the model is generalization is to unspecific.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

The Bias is defined as the grade of correctness that a learning algorithm will use. The Variance is defined as the grade of flexibility that the algorithm have given a model to learn. When having the Bias high, but the Variance low, the algorithm will not be flexible into data and will discard any data is not exactly the data that fits into the model. On the other hand, when having the variance high but the bias low, the algorithm will be very flexible into the data and will accept any error data as part of the model to learn.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

- Bias: the bias is the differnce between the predicted value and the desired value in the generalization run - Variance: is the inadequity in the produced value in the regression and the desired value that we expect from the network

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias Variance dilemma is coming from the fact that you can not have both at the same time. Your network can not be equally great at outputing with extremely high accuracy extremely hight amount of variables. Therefore you need to find balance between the two that suits needs of your neural network.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

It is refers to the problem of tryning to mantain a balance between two causes of errors in learning algorithms such that the network is able to generalize data beyong that used for training. Namely the bias error and the variance error. Having a high bias error may cause the network to miss important features in the training data, which leads to underfitting. High variance will make the network to memorize noise present in the training data rather than learning features, which lead to overfitting.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

+ One cannot optimize simultaneously the learning algorithm both for learning maximum variance in the data and learning localization which can be termed as bias.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

The Bias Variance Dilemma tells us that the bias (the difference between the actual and desired output) and the variance (output difference between each trial) cannot be decreased at the same time. A complex model results in small variance and larger variance.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

So in machine learning problem, minimizing the two main source of error simultenously does not allow the networks to be generalised very easy. If bias increase, variance decrease. And vice versa also holds. 1. Bias tells us how close we are to the true value! 2. Variance tells us how they vary for different data set. So this is a standard problem in NN

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

High value of bias means netowrk is unable to learn the data whereas higher variance means its difficult to learn the training data successfully.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias and variances are the estimation errors. Bias corresponds to the inability of the learning machine to appropriately approximate the function to be learnt. Hence this induces a deviation from the actual function Variance is the inadequacy of the training data to allow the a learning machine to succesfully learn the function. The dilemma is that , to completely learn the actual function( to reduce variance-related error), the training data required should consist of infinite samples. However, this resuts in slower convergence, inturn, bias error increases. Therefore trade of between both the errors need to be made.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias is the difference between the predicted and true value. Variance is the range of several predicted values of the same datapoint. It is desirable to have low bias and low variance to ensure the predicted value is consistently close to the true value. The Bias Variance dilemma is that to achieve low bias, the variance becomes high and vice versa. Hence, there is always a tradeoff between the two.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias variance dilemma refers to the problem of minimizing the two sources of error bias errror and variance error simultaneously which creates probblem in generaliztion of the network. Bias error: It is the error that occurs while setting the parameters of the network variance error:It refers to how sensetive the network is to the fluctuations in the dataset.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias variance dilemma is a process of simultaneously decreasing two sources of error that prevents supervised learning algorithm from generalizing beyond the trained data.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias is used to affine transform of $u$. It helps to shift the classifier line. $$v=u+b$$

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias: How close the estimate is to the true value. variance: How much does the estimate vary for different training sets. we always have either hugh variance low bias or low variance high bias.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias : differnce between the estmated output and the actual output Variance: The range of output of a network for different training set. Bias and Variance can't be decreased at the same time for many networks. ONly one at a time can be decreased

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

When adapting the parameters of a network we can either have a small bias or a small variance. If we have a small bias the approximation of the network is close to the real one, but the variance between trials is very high. If we have a low variance, the bias can't be minimized and the network has a bigger error between the apüproximation and the real value.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Ideally bias and variance would be 0 after learning a machine. However, bias and variance counteract eachother: when bias decreases, variance rises and respectively in the other direction. This leads to the dilemma that either one of the values has to be present.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Usualy only one of Bias and Variance can be minimized. In an RBFN for example few kernels with greater width leads to a high bias but a low variance. If you choose many kernels with smaller width the bias is low but the variance is high. Higher complexity models need more training data.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias is an proides an affine transformation. and it is treated a extra inputs. which noramll taken as +1

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

High bias and variance is desirable in input. Bias Variance Dilemma is the property of input data where if the bias is increased the variance decreases and vice versa. It is difficult to find a tradeoff between them.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias: Bias means how much the prediction differs from the true value Variance: Variance means how much the prediction varies for different datasets The Dilemma is that both generally can not be reduced simultaneously. A learning machine can reduce one at the cost of other.

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur

Bias-variance dilemma is a principle supervised learning problem. The dilemma arises due to the variance of data and bias of model. When there is high bias, the model fits the training data perfectly but suffers from high variance, when the bias is low the variance reduces but the model doesn’t fit the data well. This dilemma makes the generalizability difficult to achieve.

DigiKlausur