We investigate how to exploit structural similarities of an individual's potential outcomes (POs) under different treatments to obtain better estimates of conditional average treatment effects in finite samples. Especially when it is unknown whether a treatment has an effect at all, it is natural to hypothesize that the POs are similar - yet, some existing strategies for treatment effect estimation employ regularization schemes that implicitly encourage heterogeneity even when it does not exist and fail to fully make use of shared structure. In this paper, we investigate and compare three end-to-end learning strategies to overcome this problem - based on regularization, reparametrization and a flexible multi-task architecture - each encoding inductive bias favoring shared behavior across POs. To build understanding of their relative strengths, we implement all strategies using neural networks and conduct a wide range of semi-synthetic experiments. We observe that all three approaches can lead to substantial improvements upon numerous baselines and gain insight into performance differences across various experimental settings.

A novel non-parametric quantile estimation method for continuous random variables is introduced, based on a minimal neural network architecture consisting of a single unit. Its advantage over estimations from ranking the order statistics is shown, specifically for small sample size. In a regression context, the method can be used to quantify predictive uncertainty under the split conformal prediction setting, where prediction intervals are estimated from the residuals of a pre-trained model on a held-out validation set to quantify the uncertainty in future predictions. Benchmarking experiments demonstrate that the method is competitive in quality and coverage with state-of-the-art solutions, with the added benefit of being more computationally efficient.

What can be (machine) learned about the complexity of Buchberger's algorithm? Given a system of polynomials, Buchberger's algorithm computes a Gr\"obner basis of the ideal these polynomials generate using an iterative procedure based on multivariate long division. The runtime of each step of the algorithm is typically dominated by a series of polynomial additions, and the total number of these additions is a hardware independent performance metric that is often used to evaluate and optimize various implementation choices. In this work we attempt to predict, using just the starting input, the number of polynomial additions that take place during one run of Buchberger's algorithm. Good predictions are useful for quickly estimating difficulty and understanding what features make Gr\"obner basis computation hard. Our features and methods could also be used for value models in the reinforcement learning approach to optimize Buchberger's algorithm introduced in [Peifer, Stillman, and Halpern-Leistner, 2020]. We show that a multiple linear regression model built from a set of easy-to-compute ideal generator statistics can predict the number of polynomial additions somewhat well, better than an uninformed model, and better than regression models built on some intuitive commutative algebra invariants that are more difficult to compute. We also train a simple recursive neural network that outperforms these linear models. Our work serves as a proof of concept, demonstrating that predicting the number of polynomial additions in Buchberger's algorithm is a feasible problem from the point of view of machine learning.

In this paper, we investigate the question: Given a small number of datapoints, for example N = 30, how tight can PAC-Bayes and test set bounds be made? For such small datasets, test set bounds adversely affect generalisation performance by discarding data. In this setting, PAC-Bayes bounds are especially attractive, due to their ability to use all the data to simultaneously learn a posterior and bound its generalisation risk. We focus on the case of i.i.d. data with a bounded loss and consider the generic PAC-Bayes theorem of Germain et al. (2009) and Begin et al. (2016). While their theorem is known to recover many existing PAC-Bayes bounds, it is unclear what the tightest bound derivable from their framework is. Surprisingly, we show that for a fixed learning algorithm and dataset, the tightest bound of this form coincides with the tightest bound of the more restrictive family of bounds considered in Catoni (2007). In contrast, in the more natural case of distributions over datasets, we give examples (both analytic and numerical) showing that the family of bounds in Catoni (2007) can be suboptimal. Within the proof framework of Germain et al. (2009) and Begin et al. (2016), we establish a lower bound on the best bound achievable in expectation, which recovers the Chernoff test set bound in the case when the posterior is equal to the prior. Finally, to illustrate how tight these bounds can potentially be, we study a synthetic one-dimensional classification task in which it is feasible to meta-learn both the prior and the form of the bound to obtain the tightest PAC-Bayes and test set bounds possible. We find that in this simple, controlled scenario, PAC-Bayes bounds are surprisingly competitive with comparable, commonly used Chernoff test set bounds. However, the sharpest test set bounds still lead to better guarantees on the generalisation error than the PAC-Bayes bounds we consider.

Contextual bandit algorithms are useful in personalized online decision-making. However, many applications such as personalized medicine and online advertising require the utilization of individual-specific information for effective learning, while user's data should remain private from the server due to privacy concerns. This motivates the introduction of local differential privacy (LDP), a stringent notion in privacy, to contextual bandits. In this paper, we design LDP algorithms for stochastic generalized linear bandits to achieve the same regret bound as in non-privacy settings. Our main idea is to develop a stochastic gradient-based estimator and update mechanism to ensure LDP. We then exploit the flexibility of stochastic gradient descent (SGD), whose theoretical guarantee for bandit problems is rarely explored, in dealing with generalized linear bandits. We also develop an estimator and update mechanism based on Ordinary Least Square (OLS) for linear bandits. Finally, we conduct experiments with both simulation and real-world datasets to demonstrate the consistently superb performance of our algorithms under LDP constraints with reasonably small parameters $(\varepsilon, \delta)$ to ensure strong privacy protection.

When faced with learning challenging new tasks, humans often follow sequences of steps that allow them to incrementally build up the necessary skills for performing these new tasks. However, in machine learning, models are most often trained to solve the target tasks directly.Inspired by human learning, we propose a novel curriculum learning approach which decomposes challenging tasks into sequences of easier intermediate goals that are used to pre-train a model before tackling the target task. We focus on classification tasks, and design the intermediate tasks using an automatically constructed label hierarchy. We train the model at each level of the hierarchy, from coarse labels to fine labels, transferring acquired knowledge across these levels. For instance, the model will first learn to distinguish animals from objects, and then use this acquired knowledge when learning to classify among more fine-grained classes such as cat, dog, car, and truck. Most existing curriculum learning algorithms for supervised learning consist of scheduling the order in which the training examples are presented to the model. In contrast, our approach focuses on the output space of the model. We evaluate our method on several established datasets and show significant performance gains especially on classification problems with many labels. We also evaluate on a new synthetic dataset which allows us to study multiple aspects of our method.

Therefore, if the input variables (features) have a larger number The progressive development of modern technology, comprised compared to the number of training data, in some cases of computer and internet applications, generates it can result in complex and ineffective models. Basically, large amounts of data at an unprecedented speed, such the generalizability of the classifier may not be enough, as videos, photos, texts, voices, and data obtained from being necessary to extract and select features to improve the emergence of the Internet of Things (IoT) and cloud the generalizability.

K-Nearest Neighbors (KNN) search is a fundamental algorithm in artificial intelligence software with applications in robotics, and autonomous vehicles. These wide-ranging applications utilize KNN either directly for simple classification or combine KNN results as input to other algorithms such as Locally Weighted Learning (LWL). Similar to binary trees, kd-trees become unbalanced as new data is added in online applications which can lead to rapid degradation in search performance unless the tree is rebuilt. Although approximate methods are suitable for graphics applications, which prioritize query speed over query accuracy, they are unsuitable for certain applications in autonomous systems, aeronautics, and robotic manipulation where exact solutions are desired. In this paper, we will attempt to assess the performance of non-recursive deterministic kd-tree functions and KNN functions. We will also present a "forest of interval kd-trees" which reduces the number of tree rebuilds, without compromising the exactness of query results.

The adoption of machine learning in materials science has rapidly transformed materials property prediction. Hurdles limiting full capitalization of recent advancements in machine learning include the limited development of methods to learn the underlying interactions of multiple elements, as well as the relationships among multiple properties, to facilitate property prediction in new composition spaces. To address these issues, we introduce the Hierarchical Correlation Learning for Multi-property Prediction (H-CLMP) framework that seamlessly integrates (i) prediction using only a material's composition, (ii) learning and exploitation of correlations among target properties in multi-target regression, and (iii) leveraging training data from tangential domains via generative transfer learning. The model is demonstrated for prediction of spectral optical absorption of complex metal oxides spanning 69 3-cation metal oxide composition spaces. H-CLMP accurately predicts non-linear composition-property relationships in composition spaces for which no training data is available, which broadens the purview of machine learning to the discovery of materials with exceptional properties. This achievement results from the principled integration of latent embedding learning, property correlation learning, generative transfer learning, and attention models. The best performance is obtained using H-CLMP with Transfer learning (H-CLMP(T)) wherein a generative adversarial network is trained on computational density of states data and deployed in the target domain to augment prediction of optical absorption from composition. H-CLMP(T) aggregates multiple knowledge sources with a framework that is well-suited for multi-target regression across the physical sciences.

Neural forecasting has shown significant improvements in the accuracy of large-scale systems, yet predicting extremely long horizons remains a challenging task. Two common problems are the volatility of the predictions and their computational complexity; we addressed them by incorporating smoothness regularization and mixed data sampling techniques to a well-performing multi-layer perceptron based architecture (NBEATS). We validate our proposed method, DMIDAS, on high-frequency healthcare and electricity price data with long forecasting horizons (~1000 timestamps) where we improve the prediction accuracy by 5% over state-of-the-art models, reducing the number of parameters of NBEATS by nearly 70%.