Classifiers that are linear in their parameters, and trained by optimizing a convex loss function, have predictable behavior with respect to changes in the training data, initial conditions, and optimization. Such desirable properties are absent in deep neural networks (DNNs), typically trained by non-linear fine-tuning of a pre-trained model. Previous attempts to linearize DNNs have led to interesting theoretical insights, but have not impacted the practice due to the substantial performance gap compared to standard non-linear optimization. We present the first method for linearizing a pre-trained model that achieves comparable performance to non-linear fine-tuning on most of real-world image classification tasks tested, thus enjoying the interpretability of linear models without incurring punishing losses in performance. LQF consists of simple modifications to the architecture, loss function and optimization typically used for classification: Leaky-ReLU instead of ReLU, mean squared loss instead of cross-entropy, and pre-conditioning using Kronecker factorization. None of these changes in isolation is sufficient to approach the performance of non-linear fine-tuning. When used in combination, they allow us to reach comparable performance, and even superior in the low-data regime, while enjoying the simplicity, robustness and interpretability of linear-quadratic optimization.

Explanations of Machine Learning (ML) models often address a 'Why?' question. Such explanations can be related with selecting feature-value pairs which are sufficient for the prediction. Recent work has investigated explanations that address a 'Why Not?' question, i.e. finding a change of feature values that guarantee a change of prediction. Given their goals, these two forms of explaining predictions of ML models appear to be mostly unrelated. However, this paper demonstrates otherwise, and establishes a rigorous formal relationship between 'Why?' and 'Why Not?' explanations. Concretely, the paper proves that, for any given instance, 'Why?' explanations are minimal hitting sets of 'Why Not?' explanations and vice-versa. Furthermore, the paper devises novel algorithms for extracting and enumerating both forms of explanations.

Convolutional Networks have dominated the field of computer vision for the last ten years, exhibiting extremely powerful feature extraction capabilities and outstanding classification performance. The main strategy to prolong this trend relies on further upscaling networks in size. However, costs increase rapidly while performance improvements may be marginal. We hypothesise that adding heterogeneous sources of information may be more cost-effective to a CNN than building a bigger network. In this paper, an ensemble method is proposed for accurate image classification, fusing automatically detected features through Convolutional Neural Network architectures with a set of manually defined statistical indicators. Through a combination of the predictions of a CNN and a secondary classifier trained on statistical features, better classification performance can be cheaply achieved. We test multiple learning algorithms and CNN architectures on a diverse number of datasets to validate our proposal, making public all our code and data via GitHub. According to our results, the inclusion of additional indicators and an ensemble classification approach helps to increase the performance in 8 of 9 datasets, with a remarkable increase of more than 10% precision in two of them.

For developing statistical and machine learning models, it is common to split the dataset into two parts: training and testing (Stone, 1974; Hastie et al., 2009). The training part is used for fitting the model, that is, to estimate the unknown parameters in the model. The model is then evaluated for its accuracy using the testing dataset. The reason for doing this is because if we were to use the entire dataset for fitting, the model would overfit the data and can lead to poor predictions in future scenarios. Therefore, holding out a portion of the dataset and testing the model for its performance before deploying it in the field can protect against unexpected issues that can arise due to overfitting. In this article we consider only datasets where each row is independent, that is, we will exclude cases such as time series data. The simplest and probably the most common strategy to split such a dataset is to randomly sample a fraction of the dataset.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.

Is it an artist thing? That's a lot less than I expected, but I'll make it work. I see him and I hear woodwind instruments. The symmetry of him, the curve of his neck … I must take some sketches, some studies. He has that post-racial skin tone, but I can use it.

The use of genetic variants as instrumental variables - an approach known as Mendelian randomization - is a popular epidemiological method for estimating the causal effect of an exposure (phenotype, biomarker, risk factor) on a disease or health-related outcome from observational data. Instrumental variables must satisfy strong, often untestable assumptions, which means that finding good genetic instruments among a large list of potential candidates is challenging. This difficulty is compounded by the fact that many genetic variants influence more than one phenotype through different causal pathways, a phenomenon called horizontal pleiotropy. This leads to errors not only in estimating the magnitude of the causal effect but also in inferring the direction of the putative causal link. In this paper, we propose a Bayesian approach called BayesMR that is a generalization of the Mendelian randomization technique in which we allow for pleiotropic effects and, crucially, for the possibility of reverse causation. The output of the method is a posterior distribution over the target causal effect, which provides an immediate and easily interpretable measure of the uncertainty in the estimation. More importantly, we use Bayesian model averaging to determine how much more likely the inferred direction is relative to the reverse direction.

Temporal knowledge graphs (TKGs) inherently reflect the transient nature of real-world knowledge, as opposed to static knowledge graphs. Naturally, automatic TKG completion has drawn much research interests for a more realistic modeling of relational reasoning. However, most of the existing mod-els for TKG completion extend static KG embeddings that donot fully exploit TKG structure, thus lacking in 1) account-ing for temporally relevant events already residing in the lo-cal neighborhood of a query, and 2) path-based inference that facilitates multi-hop reasoning and better interpretability. In this paper, we propose T-GAP, a novel model for TKG completion that maximally utilizes both temporal information and graph structure in its encoder and decoder. T-GAP encodes query-specific substructure of TKG by focusing on the temporal displacement between each event and the query times-tamp, and performs path-based inference by propagating attention through the graph. Our empirical experiments demonstrate that T-GAP not only achieves superior performance against state-of-the-art baselines, but also competently generalizes to queries with unseen timestamps. Through extensive qualitative analyses, we also show that T-GAP enjoys from transparent interpretability, and follows human intuition in its reasoning process.

On the WikiSQL benchmark, state-of-the-art text-to-SQL systems typically take a slot-filling approach by building several dedicated models for each type of slots. Such modularized systems are not only complex butalso of limited capacity for capturing inter-dependencies among SQL clauses. To solve these problems, this paper proposes a novel extraction-linking approach, where a unified extractor recognizes all types of slot mentions appearing in the question sentence before a linker maps the recognized columns to the table schema to generate executable SQL queries. Trained with automatically generated annotations, the proposed method achieves the first place on the WikiSQL benchmark.

In this paper, we investigate an important research question in the car sequencing problem, that is, what characteristics make an instance hard to solve? To do so, we carry out an Instance Space Analysis for the car sequencing problem, by extracting a vector of problem features to characterize an instance and projecting feature vectors onto a two-dimensional space using principal component analysis. The resulting two dimensional visualizations provide insights into both the characteristics of the instances used for testing and to compare how these affect different optimisation algorithms. This guides us in constructing a new set of benchmark instances with a range of instance properties. These are shown to be both more diverse than the previous benchmarks and include many hard to solve instances. We systematically compare the performance of six algorithms for solving the car sequencing problem. The methods tested include three existing algorithms from the literature and three new ones. Importantly, we build machine learning models to identify the niche in the instance space that an algorithm is expected to perform well on. Our results show that the new algorithms are state-of-the-art. This analysis helps to understand problem hardness and select an appropriate algorithm for solving a given car sequencing problem instance.