In this paper, we develop a new classification method based on nearest centroid, and it is called the nearest disjoint centroid classifier. Our method differs from the nearest centroid classifier in the following two aspects: (1) the centroids are defined based on disjoint subsets of features instead of all the features, and (2) the distance is induced by the dimensionality-normalized norm instead of the Euclidean norm. We provide a few theoretical results regarding our method. In addition, we propose a simple algorithm based on adapted k-means clustering that can find the disjoint subsets of features used in our method, and extend the algorithm to perform feature selection. We evaluate and compare the performance of our method to other closely related classifiers on both simulated data and real-world gene expression datasets. The results demonstrate that our method is able to outperform other competing classifiers by having smaller misclassification rates and/or using fewer features in various settings and situations.

We investigate the fairness concerns of training a machine learning model using data with missing values. Even though there are a number of fairness intervention methods in the literature, most of them require a complete training set as input. In practice, data can have missing values, and data missing patterns can depend on group attributes (e.g. gender or race). Simply applying off-the-shelf fair learning algorithms to an imputed dataset may lead to an unfair model. In this paper, we first theoretically analyze different sources of discrimination risks when training with an imputed dataset. Then, we propose an integrated approach based on decision trees that does not require a separate process of imputation and learning. Instead, we train a tree with missing incorporated as attribute (MIA), which does not require explicit imputation, and we optimize a fairness-regularized objective function. We demonstrate that our approach outperforms existing fairness intervention methods applied to an imputed dataset, through several experiments on real-world datasets.

Directed networks appear in various areas, such as biology, sociology, physiology and computer science. However, at present, most network analysis ignores the direction. In this paper, we construct a spectral clustering method based on the singular decomposition of the adjacency matrix to detect community in directed stochastic block model (DiSBM). By considering a sparsity parameter, under some mild conditions, we show the proposed approach can consistently recover hidden row and column communities for different scaling of degrees. By considering the degree heterogeneity of both row and column nodes, we further establish a theoretical framework for directed degree corrected stochastic block model (DiDCSBM). We show that the spectral clustering method stably yields consistent community detection for row clusters and column clusters under mild constraints on the degree heterogeneity. Our theoretical results under DiSBM and DiDCSBM provide some innovations on some special directed networks, such as directed network with balanced clusters, directed network with nodes enjoying similar degrees, and the directed Erd\"os-R\'enyi graph. Furthermore, our theoretical results under DiDCSBM are consistent with those under DiSBM when DiDCSBM degenerates to DiSBM.

As artificial intelligence enters the legal space, it is essential to recognize biases in legal data and ensure that they are not replicated and reinforced with legal technology [7, 13, 18]. Furthermore, understanding biases in legal data and developing discrimination-free technology could help the legal space to become fairer and more widely accessible. We typically find two types of biases in legal data: First, representation biases, i.e., certain social groups are over-or underrepresented in a data set. Second, sentencing disparities, i.e., the outcome of legal proceedings for similar cases varies across social groups. Representation biases may reflect disparities in policing (arrest rates) or in offense rates.

Defining shape and form as equivalence classes under translation, rotation and -- for shapes -- also scale, we extend generalized additive regression to models for the shape/form of planar curves or landmark configurations. The model respects the resulting quotient geometry of the response, employing the squared geodesic distance as loss function and a geodesic response function mapping the additive predictor to the shape/form space. For fitting the model, we propose a Riemannian $L_2$-Boosting algorithm well-suited for a potentially large number of possibly parameter-intensive model terms, which also yiels automated model selection. We provide novel intuitively interpretable visualizations for (even non-linear) covariate effects in the shape/form space via suitable tensor based factorizations. The usefulness of the proposed framework is illustrated in an analysis of 1) astragalus shapes of wild and domesticated sheep and 2) cell forms generated in a biophysical model, as well as 3) in a realistic simulation study with response shapes and forms motivated from a dataset on bottle outlines.

Let us start with an easy example, say you are teaching a kid to differentiate dogs from cats. How would you do it? You may show him/her a dog and say "here is a dog" and when you encounter a cat you would point it out as a cat. When you show the kid enough dogs and cats, he may learn to differentiate between them. If he is trained well, he may be able to recognise different breeds of dogs which he hasn't even seen. Similarly, in Supervised Learning, we have two sets of variables.

The learning rate is often considered to be the most important hyper-parameter when training a model. Choosing the optimal learning rate can greatly improve the training of a neural network and can prevent any odd behavior that may occur during stochastic gradient descent. Stochastic gradient descent (SGD) is an optimization algorithm that helps the loss function converge to the global minimum, or where the loss is at its lowest point. It behaves just like gradient descent, but also has batches to increase the computational efficiency. Gradient descent is performed to each of these smaller batches instead of the entire training set size.

The first one helps determine any association between qualitative variables, and the second one tells whether a sample follows the same distribution as a sample or not. This test helps determine any association between two categorical values of qualitative data. It is only applicable to the Categorical data. The main task is to check whether they are not independent or how they are affecting each other. The hypothesis test carried out to check the link between the two is known as a test for independence.

Language identification is a critical component of language processing pipelines (Jauhiainen et al.,2019) and is not a solved problem in real-world settings. We present a lightweight and effective language identifier that is robust to changes of domain and to the absence of copious training data. The key idea for classification is that the reciprocal of the rank in a frequency table makes an effective additive feature score, hence the term Reciprocal Rank Classifier (RRC). The key finding for language classification is that ranked lists of words and frequencies of characters form a sufficient and robust representation of the regularities of key languages and their orthographies. We test this on two 22-language data sets and demonstrate zero-effort domain adaptation from a Wikipedia training set to a Twitter test set. When trained on Wikipedia but applied to Twitter the macro-averaged F1-score of a conventionally trained SVM classifier drops from 90.9% to 77.7%. By contrast, the macro F1-score of RRC drops only from 93.1% to 90.6%. These classifiers are compared with those from fastText and langid. The RRC performs better than these established systems in most experiments, especially on short Wikipedia texts and Twitter. The RRC classifier can be improved for particular domains and conversational situations by adding words to the ranked lists. Using new terms learned from such conversations, we demonstrate a further 7.9% increase in accuracy of sample message classification, and 1.7% increase for conversation classification. Surprisingly, this made results on Twitter data slightly worse. The RRC classifier is available as an open source Python package (https://github.com/LivePersonInc/lplangid).

Causal effect estimation for dynamic treatment regimes (DTRs) contributes to sequential decision making. However, censoring and time-dependent confounding under DTRs are challenging as the amount of observational data declines over time due to a reducing sample size but the feature dimension increases over time. Long-term follow-up compounds these challenges. Another challenge is the highly complex relationships between confounders, treatments, and outcomes, which causes the traditional and commonly used linear methods to fail. We combine outcome regression models with treatment models for high dimensional features using uncensored subjects that are small in sample size and we fit deep Bayesian models for outcome regression models to reveal the complex relationships between confounders, treatments, and outcomes. Also, the developed deep Bayesian models can model uncertainty and output the prediction variance which is essential for the safety-aware applications, such as self-driving cars and medical treatment design. The experimental results on medical simulations of HIV treatment show the ability of the proposed method to obtain stable and accurate dynamic causal effect estimation from observational data, especially with long-term follow-up. Our technique provides practical guidance for sequential decision making, and policy-making.