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Many functions characterising physical systems are additively separable. This is the case, for instance, of mechanical Hamiltonian functions in physics, population growth equations in biology, and consumer preference and utility functions in economics. We consider the scenario in which a surrogate of a function is to be tested for additive separability. The detection that the surrogate is additively separable can be leveraged to improve further learning. Hence, it is beneficial to have the ability to test for such separability in surrogates. The mathematical approach is to test if the mixed partial derivative of the surrogate is zero; or empirically, lower than a threshold. We present and comparatively and empirically evaluate the eight methods to compute the mixed partial derivative of a surrogate function.

Shortcut reasoning is an irrational process of inference, which degrades the robustness of an NLP model. While a number of previous work has tackled the identification of shortcut reasoning, there are still two major limitations: (i) a method for quantifying the severity of the discovered shortcut reasoning is not provided; (ii) certain types of shortcut reasoning may be missed. To address these issues, we propose a novel method for identifying shortcut reasoning. The proposed method quantifies the severity of the shortcut reasoning by leveraging out-of-distribution data and does not make any assumptions about the type of tokens triggering the shortcut reasoning. Our experiments on Natural Language Inference and Sentiment Analysis demonstrate that our framework successfully discovers known and unknown shortcut reasoning in the previous work.

Estimating optimal dynamic policies from offline data is a fundamental problem in dynamic decision making. In the context of causal inference, the problem is known as estimating the optimal dynamic treatment regime. Even though there exists a plethora of methods for estimation, constructing confidence intervals for the value of the optimal regime and structural parameters associated with it is inherently harder, as it involves non-linear and non-differentiable functionals of unknown quantities that need to be estimated. Prior work resorted to sub-sample approaches that can deteriorate the quality of the estimate. We show that a simple soft-max approximation to the optimal treatment regime, for an appropriately fast growing temperature parameter, can achieve valid inference on the truly optimal regime. We illustrate our result for a two-period optimal dynamic regime, though our approach should directly extend to the finite horizon case. Our work combines techniques from semi-parametric inference and $g$-estimation, together with an appropriate triangular array central limit theorem, as well as a novel analysis of the asymptotic influence and asymptotic bias of softmax approximations.

Optimizing static risk-averse objectives in Markov decision processes is difficult because they do not admit standard dynamic programming equations common in Reinforcement Learning (RL) algorithms. Dynamic programming decompositions that augment the state space with discrete risk levels have recently gained popularity in the RL community. Prior work has shown that these decompositions are optimal when the risk level is discretized sufficiently. However, we show that these popular decompositions for Conditional-Value-at-Risk (CVaR) and Entropic-Value-at-Risk (EVaR) are inherently suboptimal regardless of the discretization level. In particular, we show that a saddle point property assumed to hold in prior literature may be violated. However, a decomposition does hold for Value-at-Risk and our proof demonstrates how this risk measure differs from CVaR and EVaR. Our findings are significant because risk-averse algorithms are used in high-stake environments, making their correctness much more critical.

Linear regression adjustment is commonly used to analyse randomised controlled experiments due to its efficiency and robustness against model misspecification. Current testing and interval estimation procedures leverage the asymptotic distribution of such estimators to provide Type-I error and coverage guarantees that hold only at a single sample size. Here, we develop the theory for the anytime-valid analogues of such procedures, enabling linear regression adjustment in the sequential analysis of randomised experiments. We first provide sequential $F$-tests and confidence sequences for the parametric linear model, which provide time-uniform Type-I error and coverage guarantees that hold for all sample sizes. We then relax all linear model parametric assumptions in randomised designs and provide nonparametric model-free sequential tests and confidence sequences for treatment effects. This formally allows experiments to be continuously monitored for significance, stopped early, and safeguards against statistical malpractices in data collection. A particular feature of our results is their simplicity. Our test statistics and confidence sequences all emit closed-form expressions, which are functions of statistics directly available from a standard linear regression table. We illustrate our methodology with the sequential analysis of software A/B experiments at Netflix, performing regression adjustment with pre-treatment outcomes.

The ability to predict the behavior of a wireless channel in terms of the frame delivery ratio is quite valuable, and permits, e.g., to optimize the operating parameters of a wireless network at runtime, or to proactively react to the degradation of the channel quality, in order to meet the stringent requirements about dependability and end-to-end latency that typically characterize industrial applications. In this work, prediction models based on the exponential moving average (EMA) are investigated in depth, which are proven to outperform other simple statistical methods and whose performance is nearly as good as artificial neural networks, but with dramatically lower computational requirements. Regarding the innovation and motivation of this work, a new model that we called EMA linear combination (ELC), is introduced, explained, and evaluated experimentally. Its prediction accuracy, tested on some databases acquired from a real setup based on Wi-Fi devices, showed that ELC brings tangible improvements over EMA in any experimental conditions, the only drawback being a slight increase in computational complexity.

In conventional multiple-input multiple-output (MIMO) communication systems, the positions of antennas are fixed. To take full advantage of spatial degrees of freedom, a new technology called fluid antenna (FA) is proposed to obtain higher achievable rate and diversity gain. Most existing works on FA exploit instantaneous channel state information (CSI). However, in FA-assisted systems, it is difficult to obtain instantaneous CSI since changes in the antenna position will lead to channel variation. In this letter, we investigate a FA-assisted MIMO system using relatively slow-varying statistical CSI. Specifically, in the criterion of rate maximization, we propose an algorithmic framework for transmit precoding and transmit/receive FAs position designs with statistical CSI. Simulation results show that our proposed algorithm in FA-assisted systems significantly outperforms baselines in terms of rate performance.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.