Online Test

Introduction

• data mining from databases
  • non-trivial process of gaining implicit, previously not known, but potentially useful information from the data
  • originated in the 90s (there was not enough data before)
  • knowledge discovery in databases (KDD)
  • data mining (DM) – business intelligence (BI) and big data
• foundations
  • artificial intelligence, machine learning methods
  • database systems (to store large data sets), information retrieval
  • statistics – modeling and analysis of dependencies found in the data
  • + how to use the results for decision-making
• data mining is an interactive and iterative process
  • data preparation – we build one table containing all the relevant data
    • selection (of useful attributes), preprocessing, transformation
  • the actual “data mining” – we find patterns in the data
  • interpretation – found knowledge shall be evaluated from the point of view of the end user (manager, customer, etc.)
• PoV of a manager
  • there’s a topical issue
  • goal of the data mining process is to obtain as much information as possible that is relevant to solving the problem
  • example
    • find groups of customers of a department store to offer special services to
    • the found groups can be interpreted as segments in the given market area
  • steps
    • form a team: data analyst, domain expert, expert on databases, …
    • specify the problem
    • obtain all data available
      • we should also obtain the external data describing the environment of the analyzed processes (time period of the year, advertising, political issues, weather, …)
    • select the methods
      • clustering, classification, exploratory data analysis, association rules, decision trees, genetic algorithms, Bayesian networks, neural networks
      • visualization methods – helpful for presentation
    • preprocess the data
    • mine the data
    • interpret the results
      • we may need to create an analytical report
      • make the results easy to understand
      • the output can also mean to carry out a reasonable action
• tasks
  • classification and prediction
    • goal: predict a continuous or discrete value based on some attributes
    • interpretation may be challenging
    • prediction: weather forecast, stock prices, …
    • we should be able to cover the entire domain (all the data may be useful for a reasonable prediction)
  • description
    • goal: find a dominant structure or relationships
    • we may ignore some of the information; the extracted knowledge does not need to be that precise (but it should be easily understandable)
  • looking for “nuggets”
    • goal: find some interesting knowledge (does not have to fully cover the given concept)
• real tasks (examples)
  • segmentation and classification of bank clients
  • causes of failures in telecommunication networks
  • causes of change of service provider
  • prediction of power consumption
  • analysis of the patient database in a hospital
    • Florence Nightingale
    • Ignaz Semmelweis
  • market basket analysis

Methodologies

• goal, popular methodologies
  • goal: provide the users with a unified framework; guide data mining applications regardless of industry
  • it’s necessary to have high-quality data; the steps are usually iterative
  • popular methodologies: 5A, SEMMA, CRISPR-DM
• SEMMA
  • sample – select data for modeling
    • may include sampling, imputation (adding other useful information, e.g. adding seasons of the year to the data about the sales), partitioning (train-test-validation split)
  • explore – visual exploration and dimensionality reduction
  • modify – prepare the objects, values, and variables for data modeling; transform the data
  • model – apply data mining techniques (decision trees, regression models, NNs, …)
    • create models providing relevant outcome
  • assess – evaluate the results of modeling (assess their reliability and usefulness)
    • so that the manager can understand
• CRISP-DM
  • cross-industry standard process for data mining; a robust general-purpose model
    • software-independent
  • 6 phases (their order is not strict)
    • business understanding
      • determine our business objective
      • assess our present situation, what resources and data we have
      • risk assessment
      • setting KPIs
    • data understanding
      • collect and describe initial data; explore and visualize it
      • verify the quality of the data
    • data preparation
      • cleaning, integration (merging), aggregation, …
      • make the dataset ready for further analysis and modeling
    • modeling
      • select the modeling technique
      • generate test design
      • build the model
      • assess the model
    • evaluation
      • evaluate the results – from the point of view of the manager
      • review the process
      • determine the next steps
    • deployment
      • results should be presented in a simple and comprehensible way
      • plan the deployment (what steps should be done)
      • final report, review the project
        • to preserve knowledge
  • ciritique
    • little support for project management
    • what to do if there are problems?
    • → IBM released Analytics Solutions Unified Method for Data Mining (ASUM)
• ASUM
  • phases
    1. analyze – define the needs (desired features, performance, usability, …), obtain agreement
    2. design – define solution components, identify resources, clarify requirements
    3. configure & build – including testing and validation
    4. deploy – create a plan to run and maintain the solution
    5. operate & optimize – preserve the health
    • + project management – there are processes that help to monitor the progress and maintain the project
  • benefits
    • minimized risk
    • scalable and enterprise-ready
    • comprehensive
    • product-specific implementation roadmaps
    • users can replicate previous software implementations

Data Analysis

• types of attributes
  • interval-scaled attributes – their values are real number following a linear scale
  • ratio-scaled attributes – follow an exponential scale → need to be log-transformed ($\log x_i$) before treating them like interval-scaled attributes
  • a nominal attribute can be transformed to a series of binary attributes (one-hot encoding)
  • ordinal attributes are sometimes treated as interval-scaled attributes
• data standardization of interval-scaled attributes
  • decimal scaling – divide the data by the smallest power of 10 to get them to the interval $[-1,1]$ (while maintaining the mutual relations)
  • range standardization
    • to $[0,1]$ … $\frac{x-\mathrm{min}}{\mathrm{max}-\mathrm{min}}$
    • to $[-1,1]$ … $2\cdot \frac{x-\mathrm{min}}{\mathrm{max}-\mathrm{min}}-1$
  • Z-score standardization … $\frac{x-\mu}{\sigma}$
    • $\mu$ … mean
    • $\sigma$ … corrected sample standard deviation
      • $\sigma=\sqrt{\frac1{n-1}\sum_{i=1}^n(x_i-\mu)^2}$
    • or we can use the corrected sample standard deviation
  • standardization according to the mean absolute difference
    • $\frac{x-\mu}{s}$
    • where $s=\frac1n\sum_{i=1}^n|x_i-\mu|$
• range, quartiles, outliers
  • range = difference between the highest and the lowest value in the set
  • quartiles – values $Q_1,Q_2,Q_3$
    • 25% of the observations below $Q_1$ (lower quartile)
    • 50% below $Q_2$ (median)
    • 75% below $Q_3$ (upper quartile)
  • interquartile range $IQR=Q_3-Q_1$
  • formulas (for discrete data)
    • $Q_1=x_{\lceil n/4 \rceil}$
    • $Q_3=x_{\lceil 3n/4 \rceil}$
    • but if $x_{n/4}$ or $x_{3n/4}$ exists ($n$ is divisible by 4), we need to average this value with the next one $($$x_{n/4+1}$ or $x_{3n/4+1}$)
  • outlier is any value $\notin[Q_1-1.5\cdot IQR,\ Q_3+1.5\cdot IQR]$
  • box plot
    • box … between $Q_1$ and $Q_3$ with a mark (line) representing the median
    • two other lines … boundaries for outliers (or the extrema that are not outliers)
    • other marks outside … individual outliers
• contingency table
  • relationship between two categorical quantities (may be binary)
  • cell … how many observations have this combination of attributes
  • there are also column and row totals
  • we get an expected frequency of combination if we multiply the column total with the row total and divide it by the total number of observations
    • intuition: we take the number of elements in the column and multiply it by the (observed) probability that any sample belongs to the given row (has this value of the attribute)
• $\chi^2$-test
  • $\chi^2=\sum_k\sum_\ell\frac{(a_{k\ell}-e_{k\ell})^2}{e_{k\ell}}$
    • where $a_{k\ell}$ is the value of the cell (number of observation with this combination of attributes)
    • $e_{k\ell}$ is the expected frequency as described above: $e_{k\ell}=\frac{r_k\cdot s_\ell}n$
  • $\chi^2$ distribution has $(R-1)(S-1)$ degrees of freedom (the last row and column are somehow determined by the rest of the table)
  • we choose a level of significance $\alpha$ (usually 0.05) = probability of rejecting a true null hypothesis
  • we reject $H_0$ if our $\chi^2$-statistic is greater than the value of the $\chi^2$ distribution (for the given DoF and $\alpha$)
  • it can be used only for large-enough frequencies – when $\forall k,\ell:e_{k\ell}\geq 5$
    • if the frequencies are too low and the contingency table contains only 4 fields, we can use Fisher’s test
• Fisher’s test
  • for a contingency table with only 4 fields (two binary attributes)
  • one-sided or two-sided version
  • we get the $p$-value directly: what is the probability of this or more extreme table if we assume fixed column and row totals?
    • for the two-sided version, we need to compute the expected frequencies $e_{k\ell}$
    • probability of this table: $$p=\frac{r_1!\cdot r_2!\cdot s_1!\cdot s_2!}{n!\cdot a!\cdot b!\cdot c!\cdot d!}$$
      • $a,b,c,d$ … values of the cells
      • $r_i,s_j$ … row and column totals respectively
    • probability of some more extreme table $T_i$ – we consider values $a-i,\ b+i,\ c+i,\ d-i$ instead
    • the probabilities of the tables need to be summed up to get the $p$-value
  • null hypothesis: independence of the attributes
    • we reject for $p$-value $\leq \alpha$

Regression Analysis

• motivation
  • it may be costly to obtain output values
  • input values are known earlier than the output (we want to estimate the output)
  • controlling input variables may lead to the desired behavior of the output
  • we want to find a (causal) relationship between the input and the output
• linear regression
  • what are the parameters of the linear relationship between two numerical quantities?
  • $y=\beta x+\alpha \textcolor{gray}{+ \varepsilon}$
  • least squares method
    • find parameters $\alpha,\beta$
    • we minimize $SSE=\sum_i(y_i-f(x_i))^2$ (sum of squared errors)
    • set partial derivatives of SSE equal to zero, we get two equations:
      • $n\alpha+\beta\sum_i x_i=\sum_i y_i$
        • or $\alpha=\bar y-\beta\bar x$
      • $\alpha\sum_i x_i+\beta\sum_i x_i^2=\sum_i x_iy_i$
    • so $(\bar y-\beta\bar x)\sum_i x_i+\beta\sum_i x_i^2=\sum x_iy_i$
    • we get $\beta=\frac{\sum_i (x_i-\bar x)(y_i-\bar y)}{\sum_i(x_i-\bar x)^2}$
      • and $\alpha=\bar y-\beta\bar x$
• correlation analysis
  • is there a linear relationship between two numerical quantities?
  • correlation coefficient $\rho(x,y)=\frac{\text{cov}(x,y)}{\sigma_x\sigma_y}\in[-1,1]$
    • corrected sample covariance $\text{cov}(x,y)=\frac{1}{n-1}\sum_i(x_i-\bar x)(y_i-\bar y)$
    • corrected sample standard deviation $\sigma_x=\sqrt{\frac1{n-1}\sum_i(x_i-\bar x)^2}$
      • similar for $\sigma_y$
• multi-dimensional regression
  • linear → least-squares method in matrix form
    • $y=X\beta$
    • $X$ … matrix of input samples
      • before the $x$ values of the sample, there is $1$ (so that we don’t need to keep the constant $\alpha$)
    • so $\beta=(X^TX)^{-1}(X^Ty)$
    • may be computationally expensive → approximate solutions
  • non-linear – example: logistic regression
    • if the dependent variable is categorical
    • we use log (conditional) odds to model the conditional probability
      • $s_i=\ln\frac{P}{1-P}$
      • so $P=\frac 1{1+e^{-s_i}}$ (sigmoid)
      • where $s_i=\alpha+\beta x_i=\alpha+\sum_j\beta_j x_{ij}$
    • we estimate the parameters using maximum likelihood
      • $L=\prod_i P(y_i\mid x_i)=\prod_i p_i^{y_i}(1-p_i)^{1-y_i}$
        • $p_i=\sigma(s_i)=\frac1{1+e^{-\alpha-\beta x_i}}$
        • note that $1-p_i=1-\sigma(s_i)=\sigma(-s_i)$
      • we minimize negative log-likelihood (= cross-entropy loss)
        • $E=-\sum_i(y_i\log p_i+(1-y_i)\log(1-p_i))$
    • gradient descent is then applied like this
      • $\beta_j\leftarrow\beta_j-\eta\sum_i(\sigma(\alpha+\beta x_i)-y_i)x_{ij}$
      • $\alpha\leftarrow\alpha-\eta\sum_i(\sigma(\alpha+\beta x_i)-y_i)$
      • $\eta$ … learning rate
      • note that $\sigma'(s_i)=\sigma(s_i)(1-\sigma(s_i))$
• discriminant analysis
  • classification into classes
  • we consider a discriminant function $f_t$ for every class $c_t$
    • conditional (a posteriori) probability of classifying $x$ to the class
  • for two classes, we get $f(x)=f_1(x)-f_2(x)=P(x|c_1)P(c_1)-P(x|c_2)P(c_2)$
    • (there should be a normalization constant $\alpha$ maybe)
  • for normal distributions, we only need to estimate the means and the covariance matrices to get the discriminant functions
    • the decision boundary is located where the distribution curves intersect

Cluster Analysis

• cluster analysis, assumptions
  • we want to divide the observed samples into groups of mutually similar ones
  • assumption: we can measure the distance between samples (or between clusters)
  • distance between two samples
    • Minkovski metrics $L_z(x_1,x_2)=\sqrt[z]{\sum_j (x_{1j}-x_{2j})^z}$
      • Manhattan distance … $L_1$
      • Euclidean distance … $L_2$
      • Chebyshev distance … $L_\infty$
    • Hamming distance – number of positions at which $x_1$ and $x_2$ differ
    • Mahalanobis distance – useful if the quantities have different variance
      • uses the covariance matrix
      • $d(x_1,x_2)=(x_1-x_2)^TS^{-1}(x_1-x_2)$
  • distance between two clusters
    • method of the nearest neighbor
    • method of the farthest neighbor
    • method of average distance (we compute the mean distance of two arbitrary samples – one from each cluster)
    • centroid method (distance between the centers of the clusters)
• centroid
  • compute the average over all the features
  • but such point may not be in the data at all
• k-means clustering
  • Lloyd
    • divide the points randomly into $k$ clusters
    • repeat until convergence
      • compute the centroids
      • assign each point to its closest centroid
  • alternative initializations
    • pronounce the first $k$ points to be centroids
    • k-means++ … sample $k$ points (to be used as centroids) with probability proportional to their squared distance to the closest existing centroid
    • LocalSearch++ … start with k-means++, then sample some more points (in the same way) one by one and replace some of the existing centroids if they cover the distribution (points) better
• k-medians
  • just use Manhattan distance instead of Euclidean
  • → centroid = median (independently along each dimension)
    • the representative may not exist in the dataset
  • median is less sensitive to the presence of outliers than the mean
• hierarchical clustering
  • bottom-up approach
  • we get a dendrogram
    • a clustering corresponds to some “cut” in the dendrogram
  • algorithm
    • initialization: each point is its own cluster
    • repeat: merge the two closest clusters
• learning vector quantization (LVQ)
  • for supervised clustering
  • we consider several weight vectors (representatives)
    • each weight vector corresponds to a single class
  • first, we need to initialize the weight vectors
  • then, for every sample, we update the closest weight vector
    • if the class of the vector corresponds to the class of the sample, we move the vector closer to the sample: $w\leftarrow w+\mu(x-w)$
    • otherwise, we move it further from the sample: $w\leftarrow w-\mu(x-w)$
  • $\mu$ … learning rate (usually some constant divided by the number of the epoch)
  • no guarantee of convergence
• k-medoids
  • uses a similarity measure instead of averaging
  • we try to find $k$ best representatives $Y_1,\dots,Y_k$ (from the dataset)
    • so the medoids are real data points
  • objective function: $O=\sum_{i=1}^n(\min_j\mathrm{Dist}(X_i,Y_j))$
  • more robust to outliers than k-means
  • sometimes, we cannot easily compute average (or it does not make sense)
  • possible strategy
    • randomly select $r$ pairs $(X_i,Y_j)$ for a possible exchange
    • the pair with the best improvement of the objective function is exchanged
    • requires time proportional to $rn$
• grid-based methods
  • e.g. MAFIA
  • which cells of the grid are densely covered by the data?
  • merge neighboring dense hyper-cubes (cells) to get clusters
    • there is a threshold which tells us if the hyper-cube is dense
• density-based algorithms
  • core point: there are at least $\tau$ points closer than $\varepsilon$
  • border point: there is at least one core point closer than $\varepsilon$
  • noise point: otherwise
  • DBSCAN
    • connectivity graph
    • nodes = core points
    • nodes are connected if the core points are closer than $\varepsilon$
    • clusters = connected components
    • border points still belong to the corresponding clusters
    • noise points are reported as outliers
  • another algorithm: DENCLUE
• scalable approaches – for lots of data
  • k-medoids are expensive to compute
  • CLARA
    • based on partitioning around medoids (PAM) – a variant of k-medoids
      • all possible $k(n-k)$ pairs of medoids and non-medoids are tested for an exchange
      • the pair with the best improvement of the objective function is exchanged
      • $O(kn^2d)$ time per iteration for a $d$-dimensional dataset
    • we apply the algorithm to a smaller sample set of size $fn$ where $f\in(0,1)$
      • the remaining data points are assigned to the medoids found in the smaller sample
      • we repeat this multiple times and use the best found clustering
      • $O(kf^2n^2d+k(n-k))$ time
    • the main problem occurs when the preselected samples do not include a good choice of medoids
  • CLARANS
    • k-medoids, but uses the entire dataset
    • finds several locally optimal solutions and uses the best one
    • finding a locally optimal solution
      • randomly initialize $k$ medoids
      • repeat: take a random pair of a medoid and a non-medoid, swap them if this improves the objective function
      • if a certain number of unsuccessful exchanges is reached, we consider the solution to be locally optimal
  • CURE (clustering using representatives) – agglomerative hierarchical algorithm
    • sample $s$ points, divide them into $p$ equal partitions
    • cluster each partition independently using hierarchical merging to $k'$ clusters
    • perform hierarchical clustering over the $k'p$ clusters across all partitions to get the desired number of clusters ($k$)
    • assign each point to its closest cluster

Decision Trees

• decision tree, (dis)advantages
  • each inner node is labeled by an attribute
  • each edge is labeled by a predicate applicable to the attribute of the parent node
  • each leaf has a class label
  • there’s a stopping criterion – e.g. all the training data in the node belong to the same class
  • advantages: easy to implement and interpret, efficient, extract simple rules, applicable to large datasets
  • disadvantages
    • difficult to process continuous data (decision trees divide the features space into rectangular regions)
    • difficult to process for missing data
    • overfitting (solved by pruning)
    • mutual correlations among the attributes are not considered
      • problem if the decision boundary looks like $y=x$ (we would need to check a value of one attribute relatively to another attribute)
• top down induction of decision trees (TDIDT)
  • top-down method
  • algorithm (divide and conquer)
    • choose one attribute as a root of the subtree
    • divide the data according to the values of this attribute and add a node for each subset
    • repeat the steps recursively for any nodes that do contain data from at least two different classes
  • how to choose the attribute
    • we use Shannon entropy $H=-\sum_c p_c\log_2p_c$
      • $p_c$ … probability of occurrence of class $c$ (relative frequency of class $c$ in the data)
      • by definition, $0\log_2 0=0$
      • note that $\log_2 x=\frac{\log_{10} x}{\log_{10} 2}=\frac{\log_{10} x}{0.301}$
    • we calculate $H$ for every possible value of the attribute
    • then we apply weighted average – weights correspond to the frequencies of the values of the attribute in the data
    • we choose the attribute with the minimum weighted average entropy
      • se we choose the attribute like this: $\mathrm{argmin}_A \sum_v P(A=v) H(v)$
      • where $H(v)=-\sum_c p_c\log_2 p_c$
      • $p_c=P(C=c\mid A=v)$
      • obviously, we always consider probability $P$ estimated for the subset of the data that belongs to the current node
  • it is useful to perform early stopping (by the principle of Occam’s razor)
  • time complexity: $O(np\log p)$
    • $n$ … number of attributes
    • $p$ … number of training data
• ID3 algorithm
  • boolean output (only two classes)
  • greedy top-down method
  • divides the nodes until there is a single class or there are no attributes (or data) left
  • uses information gain = entropy reduction
    • $\mathrm{gain}(A)=H-\sum_v P(A=v)H(v)$
    • where $H$ is the entropy of the node, $H(v)$ is the entropy of the child node containing samples s.t. $A=v$
• C4.5, C5.0
  • modifications of the ID3 algorithm
  • C4.5
    • missing attribute values are ignored during tree construction; they are estimated from the other data during prediction (probably just by using mode?)
    • continuous data – categorized according to the values in the training set
    • pruning
      • train/validation split
      • subtree is replaced by a leaf (with majority vote) if the new tree does not perform worse on the validation set than the original one
      • in a similar fashion, a whole subtree can be raised (the most frequently used one)
    • rule post-pruning
      • rules can be extracted from the tree
      • then, the rules can be generalized (pruned) and ordered by their expected accuracy (then used in this order instead of the original tree)
      • quite radical pruning
      • the rules are transparent and easy to understand
    • estimates confidence interval for accuracy of rules and trees
      • for a given rule, we can evaluate training accuracy $\hat p=$ correctly classified samples ÷ all samples processed by the rule
      • we assume binomial distribution
      • for the confidence interval computed at the 95% confidence level, the lower accuracy bound for new data will correspond to $$\hat p-1.96\cdot\underbrace{\sqrt{\frac{\hat p(1-\hat p)}{N}}}_{\text{std dev}}$$
        • where $N$ is the total number of samples
    • uses information gain ratio as criterion for data division
      • $\mathrm{argmax}_A\,\frac{\mathrm{gain}(A)}{-\sum_v P(A=v)\log_2 P(A=v)}$
      • in the denominator, we have SplitInformation, which is the same formula as entropy if we consider the attribute values to be “classes”
      • this penalizes excessive branching
  • C5.0
    • commercial version of C4.5 for large databases
    • improved generation of rules
    • higher accuracy is achieved using boosting
      • we gradually construct an ensemble of several classifiers (trees)
      • every new tree tries to improve the accuracy of the ensemble
        • the (previously) incorrectly classified data points are assigned larger weights → the tree knows they have high priority
      • majority vote is used
• classification and regression trees (algorithm CART)
  • generates binary trees
    • chooses a value of an attribute it can use to split data into the two subtrees (usually it's a threshold)
  • uses entropy or Gini index to choose the best decision attribute
  • measure of “goodness” of the data division
    • $\phi(v|t)=2P_LP_R\sum_c |P(c|t_L)-P(c|t_R)|$
      • $P_L$ probability that a sample belongs to the left subtree
      • $P(c|t_L)$ probability that a sample in the left subtree belongs to class $c$
    • we want the children to be both balanced and pure
    • we use the value $v^*=\mathrm{argmax}_v\ \phi(v|t)$
  • characteristic properties of CART
    • order of the attributes corresponds to their impact during classification
    • missing data is ignored
    • stopping criterion: there's no way to divide the node in order to improve the classification accuracy
    • high accuracy achieved on the training set does not have to reflect the accuracy on the test data
• algorithm CHAID
  • chi-square automatic interaction detection
  • $\chi^2$ criterion for branching
  • values of the categorical attributes are gradually grouped together (by $\chi^2$ “similarity”) → there remain only two groups
• bagging
  • bootstrapped aggregating
  • reduces the variance of the classifier
  • if we consider an ensemble of $k$ i.i.d. classifiers with variance $\sigma^2$ each, the ensemble has variance $\sigma^2/k$
  • decision trees are an ideal choice for bagging – they have low bias and high variance (if they are sufficiently deep)
  • bagging does not reduce bias (it may even worsen accuracy if bias is the main problem)
  • to get classifiers that are i.i.d. (independent and identically distributed) to some extent, we perform bootstrapping
    • the data points are sampled uniformly from the original data with replacement
    • this way, the new dataset contains roughly $1-(1-1/n)^n\approx 1-1/e\approx 63.2\%$ distinct data points
• random forests
  • we use bagging
  • problem: pairwise correlation of models constructed using bagging
    • if our $k$ classifiers, each with variance $\sigma^2$, have a positive pairwise correlation $\rho$, then the variance of the averaged prediction will be $\rho\sigma^2+\frac{(1-\rho)\sigma^2}k$
  • solution: we limit the number of features that can be used for splitting
    • at each node, only a random subset of features is available
  • this speeds up training due to fewer features to search over at each stage and there is no need to prune the trees
  • reduced variance does not negatively affect the bias
  • two parameters
    • number of features to be sampled
    • number of trees to be built
• boosting
  • classifiers are built one by one based on a weighted dataset
    • misclassified data points tend to have larger weights
  • each new tree depends on the previous ones
    • it is trained on a dataset with different weights (it focuses on the misclassified data points)
  • in the end, we get a weighted combination of the classifiers
  • the ensemble has a lower overall bias
  • disadvantage: outliers may hurt the overall performance of the model
• random forests vs. boosting
  • random forests: fast (can run in parallel, use a small set of features at each stage)
  • boosting: sequential, can be expensive, but outperforms random forests