We propose a cross-modality manifold alignment procedure that leverages triplet loss to jointly learn consistent, multi-modal embeddings of language-based concepts of real-world items. Our approach learns these embeddings by sampling triples of anchor, positive, and negative data points from RGB-depth images and their natural language descriptions. We show that our approach can benefit from, but does not require, post-processing steps such as Procrustes analysis, in contrast to some of our baselines which require it for reasonable performance. We demonstrate the effectiveness of our approach on two datasets commonly used to develop robotic-based grounded language learning systems, where our approach outperforms four baselines, including a state-of-the-art approach, across five evaluation metrics.

Graph neural networks are powerful models for many graph-structured tasks. In this paper, we aim to solve the problem of lifelong learning for graph neural networks. One of the main challenges is the effect of "catastrophic forgetting" for continuously learning a sequence of tasks, as the nodes can only be present to the model once. Moreover, the number of nodes changes dynamically in lifelong learning and this makes many graph models and sampling strategies inapplicable. To solve these problems, we construct a new graph topology, called the feature graph. It takes features as new nodes and turns nodes into independent graphs. This successfully converts the original problem of node classification to graph classification. In this way, the increasing nodes in lifelong learning can be regarded as increasing training samples, which makes lifelong learning easier. We demonstrate that the feature graph achieves much higher accuracy than the state-of-the-art methods in both data-incremental and class-incremental tasks. We expect that the feature graph will have broad potential applications for graph-structured tasks in lifelong learning.

We present a general methodology for using unlabeled data to design semi supervised learning (SSL) variants of the Empirical Risk Minimization (ERM) learning process. Focusing on generalized linear regression, we provide a careful treatment of the effectiveness of the SSL to improve prediction performance. The key ideas are carefully considering the null model as a competitor, and utilizing the unlabeled data to determine signal-noise combinations where the SSL outperforms both the ERM learning and the null model. In the special case of linear regression with Gaussian covariates, we show that the previously suggested semi-supervised estimator is in fact not capable of improving on both the supervised estimator and the null model simultaneously. However, the new estimator presented in this work, can achieve an improvement of $O(1/n)$ term over both competitors simultaneously. On the other hand, we show that in other scenarios, such as non-Gaussian covariates, misspecified linear regression, or generalized linear regression with non-linear link functions, having unlabeled data can derive substantial improvement in prediction by applying our suggested SSL approach. Moreover, it is possible to identify the usefulness of the SSL, by using the dedicated formulas we establish throughout this work. This is shown empirically through extensive simulations.

We propose a method for combining probabilistic outputs of classifiers to make a single consensus class prediction when no further information about the individual classifiers is available, beyond that they have been trained for the same task. The lack of relevant prior information rules out typical applications of Bayesian or Dempster-Shafer methods, and the default approach here would be methods based on the principle of indifference, such as the sum or product rule, which essentially weight all classifiers equally. In contrast, our approach considers the diversity between the outputs of the various classifiers, iteratively updating predictions based on their correspondence with other predictions until the predictions converge to a consensus decision. The intuition behind this approach is that classifiers trained for the same task should typically exhibit regularities in their outputs on a new task; the predictions of classifiers which differ significantly from those of others are thus given less credence using our approach. The approach implicitly assumes a symmetric loss function, in that the relative cost of various prediction errors are not taken into account. Performance of the model is demonstrated on different benchmark datasets. Our proposed method works well in situations where accuracy is the performance metric; however, it does not output calibrated probabilities, so it is not suitable in situations where such probabilities are required for further processing.

Time-varying parameters (TVPs) models are frequently used in economics to model structural change. I show that they are in fact ridge regressions. Instantly, this makes computations, tuning, and implementation much easier than in the state-space paradigm. Among other things, solving the equivalent dual ridge problem is computationally very fast even in high dimensions, and the crucial "amount of time variation" is tuned by cross-validation. Evolving volatility is dealt with using a two-step ridge regression. I consider extensions that incorporate sparsity (the algorithm selects which parameters vary and which do not) and reduced-rank restrictions (variation is tied to a factor model). To demonstrate the usefulness of the approach, I use it to study the evolution of monetary policy in Canada. The application requires the estimation of about 4600 TVPs, a task well within the reach of the new method.

In this paper, we introduce and formalize a rank-one partitioning learning paradigm that unifies partitioning methods that proceed by summarizing a data set using a single vector that is further used to derive the final clustering partition. Using this unification as a starting point, we propose a novel algorithmic solution for the partitioning problem based on rank-one matrix factorization and denoising of piecewise constant signals. Finally, we propose an empirical demonstration of our findings and demonstrate the robustness of the proposed denoising step. We believe that our work provides a new point of view for several unsupervised learning techniques that helps to gain a deeper understanding about the general mechanisms of data partitioning.

Real estate contributes significantly to all major economies around the world. In particular, house prices have a direct impact on stakeholders, ranging from house buyers to financing companies. Thus, a plethora of techniques have been developed for real estate price prediction. Most of the existing techniques rely on different house features to build a variety of prediction models to predict house prices. Perceiving the effect of spatial dependence on house prices, some later works focused on introducing spatial regression models for improving prediction performance. However, they fail to take into account the geo-spatial context of the neighborhood amenities such as how close a house is to a train station, or a highly-ranked school, or a shopping center. Such contextual information may play a vital role in users' interests in a house and thereby has a direct influence on its price. In this paper, we propose to leverage the concept of graph neural networks to capture the geo-spatial context of the neighborhood of a house. In particular, we present a novel method, the Geo-Spatial Network Embedding (GSNE), that learns the embeddings of houses and various types of Points of Interest (POIs) in the form of multipartite networks, where the houses and the POIs are represented as attributed nodes and the relationships between them as edges. Extensive experiments with a large number of regression techniques show that the embeddings produced by our proposed GSNE technique consistently and significantly improve the performance of the house price prediction task regardless of the downstream regression model.

As Public Transport (PT) becomes more dynamic and demand-responsive, it increasingly depends on predictions of transport demand. But how accurate need such predictions be for effective PT operation? We address this question through an experimental case study of PT trips in Metropolitan Copenhagen, Denmark, which we conduct independently of any specific prediction models. First, we simulate errors in demand prediction through unbiased noise distributions that vary considerably in shape. Using the noisy predictions, we then simulate and optimize demand-responsive PT fleets via a commonly used linear programming formulation and measure their performance. Our results suggest that the optimized performance is mainly affected by the skew of the noise distribution and the presence of infrequently large prediction errors. In particular, the optimized performance can improve under non-Gaussian vs. Gaussian noise. We also obtain that dynamic routing can reduce trip time by at least 23% vs. static routing. This reduction is estimated at 809,000 EUR per year in terms of Value of Travel Time Savings for the case study.

We study the behavior of stochastic gradient descent applied to $\|Ax -b \|_2^2 \rightarrow \min$ for invertible $A \in \mathbb{R}^{n \times n}$. We show that there is an explicit constant $c_{A}$ depending (mildly) on $A$ such that $$ \mathbb{E} ~\left\| Ax_{k+1}-b\right\|^2_{2} \leq \left(1 + \frac{c_{A}}{\|A\|_F^2}\right) \left\|A x_k -b \right\|^2_{2} - \frac{2}{\|A\|_F^2} \left\|A^T A (x_k - x)\right\|^2_{2}.$$ This is a curious inequality: the last term has one more matrix applied to the residual $u_k - u$ than the remaining terms: if $x_k - x$ is mainly comprised of large singular vectors, stochastic gradient descent leads to a quick regularization. For symmetric matrices, this inequality has an extension to higher-order Sobolev spaces. This explains a (known) regularization phenomenon: an energy cascade from large singular values to small singular values smoothes.

The curse of dimensionality is a very crucial problem while dealing with real-life datasets which are generally higher-dimensional data. As the dimensionality of the feature space increases, the number of configurations can grow exponentially, and thus the number of configurations covered by an observation decreases. In such a scenario, Principal Component Analysis plays a major part in efficiently reducing the dimensionality of the data yet retaining as much as possible of the variation present in the data set. Let us give a very brief introduction to Principal Component Analysis before delving into the actual problem. The central idea of Principal Component Analysis (PCA) is to reduce the dimensionality of a data set consisting of a large number of correlated variables, while retaining the maximum possible variation present in the data set.