In an effort to improve the accuracy of credit lending decisions, many financial intuitions are now using predictions from machine learning models. While such predictions enjoy many advantages, recent research has shown that the predictions have the potential to be biased and unfair towards certain subgroups of the population. To combat this, several techniques have been introduced to help remove the bias and improve the overall fairness of the predictions. We introduce a new fairness technique, called \textit{Subgroup Threshold Optimizer} (\textit{STO}), that does not require any alternations to the input training data nor does it require any changes to the underlying machine learning algorithm, and thus can be used with any existing machine learning pipeline. STO works by optimizing the classification thresholds for individual subgroups in order to minimize the overall discrimination score between them. Our experiments on a real-world credit lending dataset show that STO can reduce gender discrimination by over 90\%.

In Precision Agriculture, the utilization of management zones (MZs) that take into account within-field variability facilitates effective fertilizer management. This approach enables the optimization of nitrogen (N) rates to maximize crop yield production and enhance agronomic use efficiency. However, existing works often neglect the consideration of responsivity to fertilizer as a factor influencing MZ determination. In response to this gap, we present a MZ clustering method based on fertilizer responsivity. We build upon the statement that the responsivity of a given site to the fertilizer rate is described by the shape of its corresponding N fertilizer-yield response (N-response) curve. Thus, we generate N-response curves for all sites within the field using a convolutional neural network (CNN). The shape of the approximated N-response curves is then characterized using functional principal component analysis. Subsequently, a counterfactual explanation (CFE) method is applied to discern the impact of various variables on MZ membership. The genetic algorithm-based CFE solves a multi-objective optimization problem and aims to identify the minimum combination of features needed to alter a site's cluster assignment. Results from two yield prediction datasets indicate that the features with the greatest influence on MZ membership are associated with terrain characteristics that either facilitate or impede fertilizer runoff, such as terrain slope or topographic aspect.

Spectral clustering is based on the spectral relaxation of the normalized/ratio graph cut criterion. While the spectral relaxation is known to be loose, it has been shown recently that a non-linear eigenproblem yields a tight relaxation of the Cheeger cut. In this paper, we extend this result considerably by providing a characterization of all balanced graph cuts which allow for a tight relaxation. Although the resulting optimization problems are non-convex and non-smooth, we provide an efficient first-order scheme which scales to large graphs. Moreover, our approach comes with the quality guarantee that given any partition as initialization the algorithm either outputs a better partition or it stops immediately.

Many machine learning and signal processing problems can be formulated as linearly constrained convex programs, which could be efficiently solved by the alternating direction method (ADM). However, usually the subproblems in ADM are easily solvable only when the linear mappings in the constraints are identities. To address this issue, we propose a linearized ADM (LADM) method by linearizing the quadratic penalty term and adding a proximal term when solving the subproblems. For fast convergence, we also allow the penalty to change adaptively according a novel update rule. We prove the global convergence of LADM with adaptive penalty (LADMAP). As an example, we apply LADMAP to solve lowrank representation (LRR), which is an important subspace clustering technique yet suffers from high computation cost.

Nonparametric Bayesian methods are developed for analysis of multi-channel spike-train data, with the feature learning and spike sorting performed jointly. The feature learning and sorting are performed simultaneously across all channels. Dictionary learning is implemented via the beta-Bernoulli process, with spike sorting performed via the dynamic hierarchical Dirichlet process (dHDP), with these two models coupled. The dHDP is augmented to eliminate refractoryperiod violations, it allows the "appearance" and "disappearance" of neurons over time, and it models smooth variation in the spike statistics.

One of the main challenges in data clustering is to define an appropriate similarity measure between two objects. Crowdclustering addresses this challenge by defining the pairwise similarity based on the manual annotations obtained through crowdsourcing. Despite its encouraging results, a key limitation of crowdclustering is that it can only cluster objects when their manual annotations are available. To address this limitation, we propose a new approach for clustering, called semi-crowdsourced clustering that effectively combines the low-level features of objects with the manual annotations of a subset of the objects obtained via crowdsourcing. The key idea is to learn an appropriate similarity measure, based on the low-level features of objects and from the manual annotations of only a small portion of the data to be clustered. One difficulty in learning the pairwise similarity measure is that there is a significant amount of noise and inter-worker variations in the manual annotations obtained via crowdsourcing. We address this difficulty by developing a metric learning algorithm based on the matrix completion method. Our empirical study with two real-world image data sets shows that the proposed algorithm outperforms state-of-the-art distance metric learning algorithms in both clustering accuracy and computational efficiency.

We introduce a new prior for use in Nonparametric Bayesian Hierarchical Clustering. The prior is constructed by marginalizing out the time information of Kingman's coalescent, providing a prior over tree structures which we call the Time-Marginalized Coalescent (TMC). This allows for models which factorize the tree structure and times, providing two benefits: more flexible priors may be constructed and more efficient Gibbs type inference can be used. We demonstrate this on an example model for density estimation and show the TMC achieves competitive experimental results.

Nonnegative Matrix Factorization (NMF) is a promising relaxation technique for clustering analysis. However, conventional NMF methods that directly approximate the pairwise similarities using the least square error often yield mediocre performance for data in curved manifolds because they can capture only the immediate similarities between data samples. Here we propose a new NMF clustering method which replaces the approximated matrix with its smoothed version using random walk. Our method can thus accommodate farther relationships between data samples. Furthermore, we introduce a novel regularization in the proposed objective function in order to improve over spectral clustering. The new learning objective is optimized by a multiplicative Majorization-Minimization algorithm with a scalable implementation for learning the factorizing matrix. Extensive experimental results on real-world datasets show that our method has strong performance in terms of cluster purity.

Learning the number of clusters is a key problem in data clustering. We present dip-means, a novel robust incremental method to learn the number of data clusters that can be used as a wrapper around any iterative clustering algorithm of k-means family. In contrast to many popular methods which make assumptions about the underlying cluster distributions, dip-means only assumes a fundamental cluster property: each cluster to admit a unimodal distribution. The proposed algorithm considers each cluster member as an individual'viewer' and applies a univariate statistic hypothesis test for unimodality (dip-test) on the distribution of distances between the viewer and the cluster members. Important advantages are: i) the unimodality test is applied on univariate distance vectors, ii) it can be directly applied with kernel-based methods, since only the pairwise distances are involved in the computations. Experimental results on artificial and real datasets indicate the effectiveness of our method and its superiority over analogous approaches.

In many graph-based machine learning and data mining approaches, the quality of the graph is critical. However, in real-world applications, especially in semisupervised learning and unsupervised learning, the evaluation of the quality of a graph is often expensive and sometimes even impossible, due the cost or the unavailability of ground truth. In this paper, we proposed a robust approach with convex optimization to "forge" a graph: with an input of a graph, to learn a graph with higher quality. Our major concern is that an ideal graph shall satisfy all the following constraints: non-negative, symmetric, low rank, and positive semidefinite. We develop a graph learning algorithm by solving a convex optimization problem and further develop an efficient optimization to obtain global optimal solutions with theoretical guarantees. With only one non-sensitive parameter, our method is shown by experimental results to be robust and achieve higher accuracy in semi-supervised learning and clustering under various settings. As a preprocessing of graphs, our method has a wide range of potential applications machine learning and data mining.