This work explores the utilization of Romanized Sinhala social media data to identify individuals at risk of depression. A machine learning-based framework is presented for the automatic screening of depression symptoms by analyzing language patterns, sentiment, and behavioural cues within a comprehensive dataset of social media posts. The research has been carried out to compare the suitability of Neural Networks over the classical machine learning techniques. The proposed Neural Network with an attention layer which is capable of handling long sequence data, attains a remarkable accuracy of 93.25% in detecting depression symptoms, surpassing current state-of-the-art methods. These findings underscore the efficacy of this approach in pinpointing individuals in need of proactive interventions and support. Mental health professionals, policymakers, and social media companies can gain valuable insights through the proposed model. Leveraging natural language processing techniques and machine learning algorithms, this work offers a promising pathway for mental health screening in the digital era. By harnessing the potential of social media data, the framework introduces a proactive method for recognizing and assisting individuals at risk of depression. In conclusion, this research contributes to the advancement of proactive interventions and support systems for mental health, thereby influencing both research and practical applications in the field.

The ability to efficiently predict adsorption properties of zeolites can be of large benefit in accelerating the design process of novel materials. The existing configuration space for these materials is wide, while existing molecular simulation methods are computationally expensive. In this work, we propose a model which is 4 to 5 orders of magnitude faster at adsorption properties compared to molecular simulations. To validate the model, we generated datasets containing various aluminium configurations for the MOR, MFI, RHO and ITW zeolites along with their heat of adsorptions and Henry coefficients for CO$_2$, obtained from Monte Carlo simulations. The predictions obtained from the Machine Learning model are in agreement with the values obtained from the Monte Carlo simulations, confirming that the model can be used for property prediction. Furthermore, we show that the model can be used for identifying adsorption sites. Finally, we evaluate the capability of our model for generating novel zeolite configurations by using it in combination with a genetic algorithm.

We study metric learning from preference comparisons under the ideal point model, in which a user prefers an item over another if it is closer to their latent ideal item. These items are embedded into $\mathbb{R}^d$ equipped with an unknown Mahalanobis distance shared across users. While recent work shows that it is possible to simultaneously recover the metric and ideal items given $\mathcal{O}(d)$ pairwise comparisons per user, in practice we often have a limited budget of $o(d)$ comparisons. We study whether the metric can still be recovered, even though it is known that learning individual ideal items is now no longer possible. We show that in general, $o(d)$ comparisons reveals no information about the metric, even with infinitely many users. However, when comparisons are made over items that exhibit low-dimensional structure, each user can contribute to learning the metric restricted to a low-dimensional subspace so that the metric can be jointly identified. We present a divide-and-conquer approach that achieves this, and provide theoretical recovery guarantees and empirical validation.

This paper studies the directed graph clustering problem through the lens of statistics, where we formulate clustering as estimating underlying communities in the directed stochastic block model (DSBM). We conduct the maximum likelihood estimation (MLE) on the DSBM and thereby ascertain the most probable community assignment given the observed graph structure. In addition to the statistical point of view, we further establish the equivalence between this MLE formulation and a novel flow optimization heuristic, which jointly considers two important directed graph statistics: edge density and edge orientation. Building on this new formulation of directed clustering, we introduce two efficient and interpretable directed clustering algorithms, a spectral clustering algorithm and a semidefinite programming based clustering algorithm. We provide a theoretical upper bound on the number of misclustered vertices of the spectral clustering algorithm using tools from matrix perturbation theory. We compare, both quantitatively and qualitatively, our proposed algorithms with existing directed clustering methods on both synthetic and real-world data, thus providing further ground to our theoretical contributions. Keywords: graph clustering, directed graphs, maximum likelihood estimation, spectral methods, matrix perturbation analysis, semidefinite programming. Authors are listed in alphabetical order. This is the corresponding author.

Tensor Networks (TNs) have recently been used to speed up kernel machines by constraining the model weights, yielding exponential computational and storage savings. In this paper we prove that the outputs of Canonical Polyadic Decomposition (CPD) and Tensor Train (TT)-constrained kernel machines recover a Gaussian Process (GP), which we fully characterize, when placing i.i.d. priors over their parameters. We analyze the convergence of both CPD and TT-constrained models, and show how TT yields models exhibiting more GP behavior compared to CPD, for the same number of model parameters. We empirically observe this behavior in two numerical experiments where we respectively analyze the convergence to the GP and the performance at prediction. We thereby establish a connection between TN-constrained kernel machines and GPs.

Learning to defer with multiple experts is a framework where the learner can choose to defer the prediction to several experts. While this problem has received significant attention in classification contexts, it presents unique challenges in regression due to the infinite and continuous nature of the label space. In this work, we introduce a novel framework of regression with deferral, which involves deferring the prediction to multiple experts. We present a comprehensive analysis for both the single-stage scenario, where there is simultaneous learning of predictor and deferral functions, and the two-stage scenario, which involves a pre-trained predictor with a learned deferral function. We introduce new surrogate loss functions for both scenarios and prove that they are supported by $H$-consistency bounds. These bounds provide consistency guarantees that are stronger than Bayes consistency, as they are non-asymptotic and hypothesis set-specific. Our framework is versatile, applying to multiple experts, accommodating any bounded regression losses, addressing both instance-dependent and label-dependent costs, and supporting both single-stage and two-stage methods. A by-product is that our single-stage formulation includes the recent regression with abstention framework (Cheng et al., 2023) as a special case, where only a single expert, the squared loss and a label-independent cost are considered. Minimizing our proposed loss functions directly leads to novel algorithms for regression with deferral. We report the results of extensive experiments showing the effectiveness of our proposed algorithms.

We present a detailed study of $H$-consistency bounds for regression. We first present new theorems that generalize the tools previously given to establish $H$-consistency bounds. This generalization proves essential for analyzing $H$-consistency bounds specific to regression. Next, we prove a series of novel $H$-consistency bounds for surrogate loss functions of the squared loss, under the assumption of a symmetric distribution and a bounded hypothesis set. This includes positive results for the Huber loss, all $\ell_p$ losses, $p \geq 1$, the squared $\epsilon$-insensitive loss, as well as a negative result for the $\epsilon$-insensitive loss used in squared Support Vector Regression (SVR). We further leverage our analysis of $H$-consistency for regression and derive principled surrogate losses for adversarial regression (Section 5). This readily establishes novel algorithms for adversarial regression, for which we report favorable experimental results in Section 6.

Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian counterpart. In this work we present a promising approach to address this challenge, based on the hypothesis that commonly used ML algorithms are efficient across a wide variety of tasks and may thus be near Bayes-optimal w.r.t. an unknown task distribution. We prove that it is possible to recover the Bayesian posterior defined by the task distribution, which is unknown but optimal in this setting, by building a martingale posterior using the algorithm. We further propose a practical uncertainty quantification method that apply to general ML algorithms. Experiments based on a variety of non-NN and NN algorithms demonstrate the efficacy of our method.

Important examples are given by hyperparameter optimization and meta-learning (Franceschi et al., 2018; Lee et al., 2019), where (1) expresses the optimality conditions of a lower-level minimization problem. Further examples include learning a surrogate model for data poisoning attacks (Xiao et al., 2015; Muñoz-González et al., 2017), deep equilibrium models (Bai et al., 2019) or OptNet (Amos & Kolter, 2017). All these problems may present nonsmooth mappings Φ. For instance, consider hyperparameter optimization or data poisoning attacks for SVMs, or meta-learning for image classification, where Φ is evaluated through the forward pass of a neural net with RELU activations (Bertinetto et al., 2019; Lee et al., 2019; Rajeswaran et al., 2019). In addition, when such settings are applied to large datasets, evaluating the map Φ would be too costly, but we can usually apply stochastic methods through the composite stochastic structure in (2), where only T involves a computation on the full training set (e.g., a gradient descent step).

Recent works have shown that line search methods greatly increase performance of traditional stochastic gradient descent methods on a variety of datasets and architectures [1], [2]. In this work we succeed in extending line search methods to the novel and highly popular Transformer architecture and dataset domains in natural language processing. More specifically, we combine the Armijo line search with the Adam optimizer and extend it by subdividing the networks architecture into sensible units and perform the line search separately on these local units. Our optimization method outperforms the traditional Adam optimizer and achieves significant performance improvements for small data sets or small training budgets, while performing equal or better for other tested cases. Our work is publicly available as a python package, which provides a hyperparameter-free pytorch optimizer that is compatible with arbitrary network architectures.