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The goal of high-utility sequential pattern mining (HUSPM) is to efficiently discover profitable or useful sequential patterns in a large number of sequences. However, simply being aware of utility-eligible patterns is insufficient for making predictions. To compensate for this deficiency, high-utility sequential rule mining (HUSRM) is designed to explore the confidence or probability of predicting the occurrence of consequence sequential patterns based on the appearance of premise sequential patterns. It has numerous applications, such as product recommendation and weather prediction. However, the existing algorithm, known as HUSRM, is limited to extracting all eligible rules while neglecting the correlation between the generated sequential rules. To address this issue, we propose a novel algorithm called correlated high-utility sequential rule miner (CoUSR) to integrate the concept of correlation into HUSRM. The proposed algorithm requires not only that each rule be correlated but also that the patterns in the antecedent and consequent of the high-utility sequential rule be correlated. The algorithm adopts a utility-list structure to avoid multiple database scans. Additionally, several pruning strategies are used to improve the algorithm's efficiency and performance. Based on several real-world datasets, subsequent experiments demonstrated that CoUSR is effective and efficient in terms of operation time and memory consumption.

The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC space, which may include the FPRs with no practical relevance in some applications. The partial AUC, as a generalization of the AUC, summarizes only the TPRs over a specific range of the FPRs and is thus a more suitable performance measure in many real-world situations. Although partial AUC optimization in a range of FPRs had been studied, existing algorithms are not scalable to big data and not applicable to deep learning. To address this challenge, we cast the problem into a non-smooth difference-of-convex (DC) program for any smooth predictive functions (e.g., deep neural networks), which allowed us to develop an efficient approximated gradient descent method based on the Moreau envelope smoothing technique, inspired by recent advances in non-smooth DC optimization. To increase the efficiency of large data processing, we used an efficient stochastic block coordinate update in our algorithm. Our proposed algorithm can also be used to minimize the sum of ranked range loss, which also lacks efficient solvers. We established a complexity of $\tilde O(1/\epsilon^6)$ for finding a nearly $\epsilon$-critical solution. Finally, we numerically demonstrated the effectiveness of our proposed algorithms for both partial AUC maximization and sum of ranked range loss minimization.

Search engines and recommendation systems are built to efficiently display relevant information from those massive amounts of candidates. Typically a three-stage mechanism is employed in those systems: (i) a small collection of items are first retrieved by (e.g.,) approximate near neighbor search algorithms; (ii) then a collection of constraints are applied on the retrieved items; (iii) a fine-grained ranking neural network is employed to determine the final recommendation. We observe a major defect of the original three-stage pipeline: Although we only target to retrieve $k$ vectors in the final recommendation, we have to preset a sufficiently large $s$ ($s > k$) for each query, and ``hope'' the number of survived vectors after the filtering is not smaller than $k$. That is, at least $k$ vectors in the $s$ similar candidates satisfy the query constraints. In this paper, we investigate this constrained similarity search problem and attempt to merge the similarity search stage and the filtering stage into one single search operation. We introduce AIRSHIP, a system that integrates a user-defined function filtering into the similarity search framework. The proposed system does not need to build extra indices nor require prior knowledge of the query constraints. We propose three optimization strategies: (1) starting point selection, (2) multi-direction search, and (3) biased priority queue selection. Experimental evaluations on both synthetic and real data confirm the effectiveness of the proposed AIRSHIP algorithm. We focus on constrained graph-based approximate near neighbor (ANN) search in this study, in part because graph-based ANN is known to achieve excellent performance. We believe it is also possible to develop constrained hashing-based ANN or constrained quantization-based ANN.

Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not), and for identifying strategies for regularization or efficiency improvements. Despite recent progress, e.g., comparing vision transformers to CNNs, systematic comparison of function, especially across different networks, remains difficult and is often carried out layer by layer. Approaches such as canonical correlation analysis (CCA) are applicable in principle, but have been sparingly used so far. In this paper, we revisit a (less widely known) from statistics, called distance correlation (and its partial variant), designed to evaluate correlation between feature spaces of different dimensions. We describe the steps necessary to carry out its deployment for large scale models -- this opens the door to a surprising array of applications ranging from conditioning one deep model w.r.t. another, learning disentangled representations as well as optimizing diverse models that would directly be more robust to adversarial attacks. Our experiments suggest a versatile regularizer (or constraint) with many advantages, which avoids some of the common difficulties one faces in such analyses. Code is at //github.com/zhenxingjian/Partial_Distance_Correlation.

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the algorithms cannot handle weighted data samples. Specifically, they rely on the discreteness of the loss function, which means that real-valued weights cannot be directly used. For example, none of the existing techniques produce policies that incorporate inverse propensity weighting on individual data points. We present three algorithms for efficient sparse weighted decision tree optimization. The first approach directly optimizes the weighted loss function; however, it tends to be computationally inefficient for large datasets. Our second approach, which scales more efficiently, transforms weights to integer values and uses data duplication to transform the weighted decision tree optimization problem into an unweighted (but larger) counterpart. Our third algorithm, which scales to much larger datasets, uses a randomized procedure that samples each data point with a probability proportional to its weight. We present theoretical bounds on the error of the two fast methods and show experimentally that these methods can be two orders of magnitude faster than the direct optimization of the weighted loss, without losing significant accuracy.

Current treatment planning of patients diagnosed with a brain tumor, such as glioma, could significantly benefit by accessing the spatial distribution of tumor cell concentration. Existing diagnostic modalities, e.g. magnetic resonance imaging (MRI), contrast sufficiently well areas of high cell density. In gliomas, however, they do not portray areas of low cell concentration, which can often serve as a source for the secondary appearance of the tumor after treatment. To estimate tumor cell densities beyond the visible boundaries of the lesion, numerical simulations of tumor growth could complement imaging information by providing estimates of full spatial distributions of tumor cells. Over recent years a corpus of literature on medical image-based tumor modeling was published. It includes different mathematical formalisms describing the forward tumor growth model. Alongside, various parametric inference schemes were developed to perform an efficient tumor model personalization, i.e. solving the inverse problem. However, the unifying drawback of all existing approaches is the time complexity of the model personalization which prohibits a potential integration of the modeling into clinical settings. In this work, we introduce a deep learning based methodology for inferring the patient-specific spatial distribution of brain tumors from T1Gd and FLAIR MRI medical scans. Coined as Learn-Morph-Infer the method achieves real-time performance in the order of minutes on widely available hardware and the compute time is stable across tumor models of different complexity, such as reaction-diffusion and reaction-advection-diffusion models. We believe the proposed inverse solution approach not only bridges the way for clinical translation of brain tumor personalization but can also be adopted to other scientific and engineering domains.

The common methods of spectral analysis for multivariate ($n$-dimensional) time series, like discrete Frourier transform (FT) or Wavelet transform, are based on Fourier series to decompose discrete data into a set of trigonometric model components, e. g. amplitude and phase. Applied to discrete data with a finite range several limitations of (time discrete) FT can be observed which are caused by the orthogonality mismatch of the trigonometric basis functions on a finite interval. However, in the general situation of non-equidistant or fragmented sampling FT based methods will cause significant errors in the parameter estimation. Therefore, the classical Lomb-Scargle method (LSM), which is not based on Fourier series, was developed as a statistical tool for one dimensional data to circumvent the inconsistent and erroneous parameter estimation of FT. The present work deduces LSM for $n$-dimensional data sets by a redefinition of the shifting parameter $\tau$, to maintain orthogonality of the trigonometric basis. An analytical derivation shows, that $n$-D LSM extents the traditional 1D case preserving all the statistical benefits, such as the improved noise rejection. Here, we derive the parameter confidence intervals for LSM and compare it with FT. Applications with ideal test data and experimental data will illustrate and support the proposed method.

Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.

Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.

Meta-learning extracts the common knowledge acquired from learning different tasks and uses it for unseen tasks. It demonstrates a clear advantage on tasks that have insufficient training data, e.g., few-shot learning. In most meta-learning methods, tasks are implicitly related via the shared model or optimizer. In this paper, we show that a meta-learner that explicitly relates tasks on a graph describing the relations of their output dimensions (e.g., classes) can significantly improve the performance of few-shot learning. This type of graph is usually free or cheap to obtain but has rarely been explored in previous works. We study the prototype based few-shot classification, in which a prototype is generated for each class, such that the nearest neighbor search between the prototypes produces an accurate classification. We introduce "Gated Propagation Network (GPN)", which learns to propagate messages between prototypes of different classes on the graph, so that learning the prototype of each class benefits from the data of other related classes. In GPN, an attention mechanism is used for the aggregation of messages from neighboring classes, and a gate is deployed to choose between the aggregated messages and the message from the class itself. GPN is trained on a sequence of tasks from many-shot to few-shot generated by subgraph sampling. During training, it is able to reuse and update previously achieved prototypes from the memory in a life-long learning cycle. In experiments, we change the training-test discrepancy and test task generation settings for thorough evaluations. GPN outperforms recent meta-learning methods on two benchmark datasets in all studied cases.