Understanding temporal dynamics has proved to be highly valuable for accurate recommendation. Sequential recommenders have been successful in modeling the dynamics of users and items over time. However, while different model architectures excel at capturing various temporal ranges or dynamics, distinct application contexts require adapting to diverse behaviors. In this paper we examine how to build a model that can make use of different temporal ranges and dynamics depending on the request context. We begin with the analysis of an anonymized Youtube dataset comprising millions of user sequences. We quantify the degree of long-range dependence in these sequences and demonstrate that both short-term and long-term dependent behavioral patterns co-exist. We then propose a neural Multi-temporal-range Mixture Model (M3) as a tailored solution to deal with both short-term and long-term dependencies. Our approach employs a mixture of models, each with a different temporal range. These models are combined by a learned gating mechanism capable of exerting different model combinations given different contextual information. In empirical evaluations on a public dataset and our own anonymized YouTube dataset, M3 consistently outperforms state-of-the-art sequential recommendation methods.

An ever-looming threat to astronomical applications of machine learning is the danger of over-fitting data, also known as the `curse of dimensionality.' This occurs when there are fewer samples than the number of independent variables. In this work, we focus on the problem of stellar parameterization from low-mid resolution spectra, with blended absorption lines. We address this problem using an iterative algorithm to sequentially prune redundant features from synthetic PHOENIX spectra, and arrive at an optimal set of wavelengths with the strongest correlation with each of the output variables -- T$_{\rm eff}$, $\log g$, and [Fe/H]. We find that at any given resolution, most features (i.e., absorption lines) are not only redundant, but actually act as noise and decrease the accuracy of parameter retrieval.

We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space (WL-RKHS) for nonlinear regression and complex-valued signals, recently proposed by the authors. This paper shows that in the adaptive version of the kernel regression for complex-valued signals we need to include another kernel term, the so-called pseudo-kernel. This new solution is endowed with better representation capabilities in complex-valued fields, since it can efficiently decouple the learning of the real and the imaginary part. Also, we review previous realizations of the complex KLMS algorithm and its augmented version to prove that they can be rewritten as particular cases of the gCKLMS. Furthermore, important conclusions on the kernels design are drawn that help to greatly improve the convergence of the algorithms. In the experiments, we revisit the nonlinear channel equalization problem to highlight the better convergence of the gCKLMS compared to previous solutions. Also, the flexibility of the proposed generalized approach is tested in a second experiment with non-independent real and imaginary parts. The results illustrate the significant performance improvements of the gCKLMS approach when the complex-valued signals have different properties for the real and imaginary parts.

While stochastic gradient descent (SGD) is one of the major workhorses in machine learning, the learning properties of many practically used variants are poorly understood. In this paper, we consider least squares learning in a nonparametric setting and contribute to filling this gap by focusing on the effect and interplay of multiple passes, mini-batching and averaging, and in particular tail averaging. Our results show how these different variants of SGD can be combined to achieve optimal learning errors, hence providing practical insights. In particular, we show for the first time in the literature that tail averaging allows faster convergence rates than uniform averaging in the nonparametric setting. Finally, we show that a combination of tail-averaging and minibatching allows more aggressive step-size choices than using any one of said components.

In this paper, we propose a novel hash learning approach that has the following main distinguishing features, when compared to past frameworks. First, the codewords are utilized in the Hamming space as ancillary techniques to accomplish its hash learning task. These codewords, which are inferred from the data, attempt to capture grouping aspects of the data's hash codes. Furthermore, the proposed framework is capable of addressing supervised, unsupervised and, even, semi-supervised hash learning scenarios. Additionally, the framework adopts a regularization term over the codewords, which automatically chooses the codewords for the problem. To efficiently solve the problem, one Block Coordinate Descent algorithm is showcased in the paper. We also show that one step of the algorithms can be casted into several Support Vector Machine problems which enables our algorithms to utilize efficient software package. For the regularization term, a closed form solution of the proximal operator is provided in the paper. A series of comparative experiments focused on content-based image retrieval highlights its performance advantages.

We propose $\beta$-graph embedding for robustly learning feature vectors from data vectors and noisy link weights. A newly introduced empirical moment $\beta$-score reduces the influence of contamination and robustly measures the difference between the underlying correct expected weights of links and the specified generative model. The proposed method is computationally tractable; we employ a minibatch-based efficient stochastic algorithm and prove that this algorithm locally minimizes the empirical moment $\beta$-score. We conduct numerical experiments on synthetic and real-world datasets.

In unsupervised domain adaptation, it is widely known that the target domain error can be provably reduced by having a shared input representation that makes the source and target domains indistinguishable from each other. Very recently it has been studied that not just matching the marginal input distributions, but the alignment of output (class) distributions is also critical. The latter can be achieved by minimizing the maximum discrepancy of predictors (classifiers). In this paper, we adopt this principle, but propose a more systematic and effective way to achieve hypothesis consistency via Gaussian processes (GP). The GP allows us to define/induce a hypothesis space of the classifiers from the posterior distribution of the latent random functions, turning the learning into a simple large-margin posterior separation problem, far easier to solve than previous approaches based on adversarial minimax optimization. We formulate a learning objective that effectively pushes the posterior to minimize the maximum discrepancy. This is further shown to be equivalent to maximizing margins and minimizing uncertainty of the class predictions in the target domain, a well-established principle in classical (semi-)supervised learning. Empirical results demonstrate that our approach is comparable or superior to the existing methods on several benchmark domain adaptation datasets.

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature mapping, they are still subject to cubic cost on the number of points. Given only a few thousand locations, this computational cost rapidly outstrips the currently available computational power. This paper aims to provide an overview of kernel methods from first-principals (with a focus on ridge regression), before progressing to a review of random Fourier features (RFF), a set of methods that enable the scaling of kernel methods to big datasets. At each stage, the associated R code is provided. We begin by illustrating how the dual representation of ridge regression relies solely on inner products and permits the use of kernels to map the data into high-dimensional spaces. We progress to RFFs, showing how only a few lines of code provides a significant computational speed-up for a negligible cost to accuracy. We provide an example of the implementation of RFFs on a simulated spatial data set to illustrate these properties. Lastly, we summarise the main issues with RFFs and highlight some of the advanced techniques aimed at alleviating them.

Background: The problem of predicting whether a drug combination of arbitrary orders is likely to induce adverse drug reactions is considered in this manuscript. Methods: Novel kernels over drug combinations of arbitrary orders are developed within support vector machines for the prediction. Graph matching methods are used in the novel kernels to measure the similarities among drug combinations, in which drug co-medication patterns are leveraged to measure single drug similarities. Results: The experimental results on a real-world dataset demonstrated that the new kernels achieve an area under the curve (AUC) value 0.912 for the prediction problem. Conclusions: The new methods with drug co-medication based single drug similarities can accurately predict whether a drug combination is likely to induce adverse drug reactions of interest. Keywords: drug-drug interaction prediction; drug combination similarity; co-medication; graph matching

We introduce the Neural Conditioner (NC), a self-supervised machine able to learn about all the conditional distributions of a random vector $X$. The NC is a function $NC(x \cdot a, a, r)$ that leverages adversarial training to match each conditional distribution $P(X_r|X_a=x_a)$. After training, the NC generalizes to sample from conditional distributions never seen, including the joint distribution. The NC is also able to auto-encode examples, providing data representations useful for downstream classification tasks. In sum, the NC integrates different self-supervised tasks (each being the estimation of a conditional distribution) and levels of supervision (partially observed data) seamlessly into a single learning experience.