World Input-Output (I/O) matrices provide the networks of within- and cross-country economic relations. In the context of I/O analysis, the methodology adopted by national statistical offices in data collection raises the issue of obtaining reliable data in a timely fashion and it makes the reconstruction of (part of) the I/O matrices of particular interest. In this work, we propose a method combining hierarchical clustering and Matrix Completion (MC) with a LASSO-like nuclear norm penalty, to impute missing entries of a partially unknown I/O matrix. Through simulations based on synthetic matrices we study the effectiveness of the proposed method to predict missing values from both previous years data and current data related to countries similar to the one for which current data are obscured. To show the usefulness of our method, an application based on World Input-Output Database (WIOD) tables - which are an example of industry-by-industry I/O tables - is provided. Strong similarities in structure between WIOD and other I/O tables are also found, which make the proposed approach easily generalizable to them.

Unsupervised semantic segmentation aims to discover and localize semantically meaningful categories within image corpora without any form of annotation. To solve this task, algorithms must produce features for every pixel that are both semantically meaningful and compact enough to form distinct clusters. Unlike previous works which achieve this with a single end-to-end framework, we propose to separate feature learning from cluster compactification. Empirically, we show that current unsupervised feature learning frameworks already generate dense features whose correlations are semantically consistent. This observation motivates us to design STEGO (Self-supervised Transformer with Energy-based Graph Optimization), a novel framework that distills unsupervised features into highquality discrete semantic labels. At the core of STEGO is a novel contrastive loss function that encourages features to form compact clusters while preserving their relationships across the corpora. STEGO yields a significant improvement over the prior state of the art, on both the CocoStuff (+14 mIoU) and Cityscapes (+9 mIoU) semantic segmentation challenges. Semantic segmentation is the process of classifying each individual pixel of an image into a known ontology. Though semantic segmentation models can detect and delineate objects at a much finer granularity than classification or object detection systems, these systems are hindered by the difficulties of creating labelled training data. In particular, segmenting an image can take over 100 more effort for a human annotator than classifying or drawing bounding boxes (Zlateski et al., 2018). Furthermore, in complex domains such as medicine, biology, or astrophysics, ground-truth segmentation labels may be unknown, ill-defined, or require considerable domain-expertise to provide (Yu et al., 2018). Recently, several works introduced semantic segmentation systems that could learn from weaker forms of labels such as classes, tags, bounding boxes, scribbles, or point annotations (Ren et al., 2020; Pan et al., 2021; Liu et al., 2020; Bilen et al.). However, comparatively few works take up the challenge of semantic segmentation without any form of human supervision or motion cues.

Local explanations of learning-to-rank (LTR) models are thought to extract the most important features that contribute to the ranking predicted by the LTR model for a single data point. Evaluating the accuracy of such explanations is challenging since the ground truth feature importance scores are not available for most modern LTR models. In this work, we propose a systematic evaluation technique for explanations of LTR models. Instead of using black-box models, such as neural networks, we propose to focus on tree-based LTR models, from which we can extract the ground truth feature importance scores using decision paths. Once extracted, we can directly compare the ground truth feature importance scores to the feature importance scores generated with explanation techniques. We compare two recently proposed explanation techniques for LTR models when using decision trees and gradient boosting models on the MQ2008 dataset. We show that the explanation accuracy in these techniques can largely vary depending on the explained model and even which data point is explained.

Time and seasonality features are often assumed in time series analysis, ignoring their crucial role as an input in model calibration. More recently cyclic seasonality variables have become highly popular in data science. Finding the optimal form of seasonality effects however should be part of the model-building process, and not simply taken for granted. Cyclic seasonality features through trigonometric sine and cosine transformations have long been used in biomedical and ecology research. The intuition behind them is that time is cyclical. A plot of the trigonometric transformation of hours is shown below.

Approximate learning machines have become popular in the era of small devices, including quantised, factorised, hashed, or otherwise compressed predictors, and the quest to explain and guarantee good generalisation abilities for such methods has just begun. In this paper we study the role of approximability in learning, both in the full precision and the approximated settings of the predictor that is learned from the data, through a notion of sensitivity of predictors to the action of the approximation operator at hand. We prove upper bounds on the generalisation of such predictors, yielding the following main findings, for any PAC-learnable class and any given approximation operator. 1) We show that under mild conditions, approximable target concepts are learnable from a smaller labelled sample, provided sufficient unlabelled data. 2) We give algorithms that guarantee a good predictor whose approximation also enjoys the same generalisation guarantees. 3) We highlight natural examples of structure in the class of sensitivities, which reduce, and possibly even eliminate the otherwise abundant requirement of additional unlabelled data, and henceforth shed new light onto what makes one problem instance easier to learn than another. These results embed the scope of modern model compression approaches into the general goal of statistical learning theory, which in return suggests appropriate algorithms through minimising uniform bounds.

We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the iterative working of the algorithm, in the sense that the partitions of the hierarchical clusters are purely defined in accordance with the input dataset. Our method is a universal hierarchical clustering approach since it can be implemented as bottom up or top down versions, both of which result in the same clustering. We show that for certain types of datasets, our algorithm has near-linear time and space complexity.

Periodic time series (PTS) forecasting plays a crucial role in a variety of industries to foster critical tasks, such as early warning, pre-planning, resource scheduling, etc. However, the complicated dependencies of the PTS signal on its inherent periodicity as well as the sophisticated composition of various periods hinder the performance of PTS forecasting. In this paper, we introduce a deep expansion learning framework, DEPTS, for PTS forecasting. DEPTS starts with a decoupled formulation by introducing the periodic state as a hidden variable, which stimulates us to make two dedicated modules to tackle the aforementioned two challenges. First, we develop an expansion module on top of residual learning to perform a layer-by-layer expansion of those complicated dependencies. Second, we introduce a periodicity module with a parameterized periodic function that holds sufficient capacity to capture diversified periods. Moreover, our two customized modules also have certain interpretable capabilities, such as attributing the forecasts to either local momenta or global periodicity and characterizing certain core periodic properties, e.g., amplitudes and frequencies. Extensive experiments on both synthetic data and real-world data demonstrate the effectiveness of DEPTS on handling PTS. In most cases, DEPTS achieves significant improvements over the best baseline. Specifically, the error reduction can even reach up to 20% for a few cases. Finally, all codes are publicly available.

"Good features allow a simple model to beat a complex model" We'll see there's an almost infinite number of ways to build new features from existing ones, so the art in Feature Generation, once you're aware of the basic techniques described below, is really in gaining the intuition on what to try. For this article, we'll be jointly describing both Feature Extraction, which generally refers to domain-specific methods of dimensionality reduction, as well as Feature Generation, accomplished via i. mapping existing features into a new space, ii. We'll be grouping methods by their applicability to the underlying data type. The periodicity may manifest at more than one time-scale so, depending on your data, you may wish to decompose a timestamp column into multiple columns, such as: Minutes, Hour, Day of week, Weekday-or-Weekend, Day of Month, Month, Season or Year. Doing so will also let you use pd.DataFrame.groupby() to perform aggregations, which is in itself one of the most powerful ways to generate new features.

There are many types of algorithms you can use, so it can be quite overwhelming which one to choose and which one is the right fit for your task. A good way to distinguish between the different types of algorithms is through their type of learning and the task at hand. I will be going through different types of classification algorithms. But first, let's understand the different types of learning within Machine Learning. Supervised Learning is when the algorithm learns on a labeled dataset and analyses the training data.

In machine learning, optimization of the results produced by models plays an important role in obtaining better results. We normally get these results in tabular form and optimizing models using such tabular results makes the procedure complex and time-consuming. Visualizing results in a good manner is very helpful in model optimization. Using the PyCaret library, we can visualize the results and optimize them. In this article, we are going to discuss how we can visualize results from different modelling procedures.