It is well-known that the distribution over functions induced through a zero-mean iid prior distribution over the parameters of a multi-layer perceptron (MLP) converges to a Gaussian process (GP), under mild conditions. We extend this result firstly to independent priors with general zero or non-zero means, and secondly to a family of partially exchangeable priors which generalise iid priors. We discuss how the second prior arises naturally when considering an equivalence class of functions in an MLP and through training processes such as stochastic gradient descent. The model resulting from partially exchangeable priors is a GP, with an additional level of inference in the sense that the prior and posterior predictive distributions require marginalisation over hyperparameters. We derive the kernels of the limiting GP in deep MLPs, and show empirically that these kernels avoid certain pathologies present in previously studied priors. We empirically evaluate our claims of convergence by measuring the maximum mean discrepancy between finite width models and limiting models. We compare the performance of our new limiting model to some previously discussed models on synthetic regression problems. We observe increasing ill-conditioning of the marginal likelihood and hyper-posterior as the depth of the model increases, drawing parallels with finite width networks which require notoriously involved optimisation tricks.

We propose an efficient distributed online learning protocol for low-latency real-time services. It extends a previously presented protocol to kernelized online learners that represent their models by a support vector expansion. While such learners often achieve higher predictive performance than their linear counterparts, communicating the support vector expansions becomes inefficient for large numbers of support vectors. The proposed extension allows for a larger class of online learning algorithms---including those alleviating the problem above through model compression. In addition, we characterize the quality of the proposed protocol by introducing a novel criterion that requires the communication to be bounded by the loss suffered.

The majority of cancer treatments end in failure due to Intra-Tumor Heterogeneity (ITH). ITH in cancer is represented by clonal evolution where different sub-clones compete with each other for resources under conditions of Darwinian natural selection. Predicting the growth of these sub-clones within a tumour is among the key challenges of modern cancer research. Predicting tumor behavior enables the creation of risk profiles for patients and the optimisation of their treatment by therapeutically targeting sub-clones more likely to grow. Current research efforts in this space are focused on mathematical modelling of population genetics to quantify the selective advantage of sub-clones, thus enabling predictions of which sub-clones are more likely to grow. These tumor evolution models are based on assumptions which are not valid for real-world tumor micro-environment. Furthermore, these models are often fit on a single instance of a tumor, and hence prediction models cannot be validated. This paper presents an alternative approach for predicting cancer evolution using a data-driven machine learning method. Our proposed method is based on the intuition that if we can capture the true characteristics of sub-clones within a tumor and represent it in the form of features, a sophisticated machine learning algorithm can be trained to predict its behavior. The work presented here provides a novel approach to predicting cancer evolution, utilizing a data-driver approach. We strongly believe that the accumulation of data from microbiologists, oncologists and machine learning researchers could be used to encapsulate the true essence of tumor sub-clones, and can play a vital role in selecting the best cancer treatments for patients.

The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the computational burden of the principal support vector machines method constrains its use for massive data. To address this issue, we in this paper propose two distributed estimation algorithms for fast implementation when the sample size is large. Both the two distributed sufficient dimension reduction estimators enjoy the same statistical efficiency as merging all the data together, which provides rigorous statistical guarantees for their application to large scale datasets. The two distributed algorithms are further adapt to principal weighted support vector machines (Shin et al., 2016) for sufficient dimension reduction in binary classification. The statistical accuracy and computational complexity of our proposed methods are examined through comprehensive simulation studies and a real data application with more than 600000 samples.

The Tsetlin Machine (TM) is an interpretable mechanism for pattern recognition that constructs conjunctive clauses from data. The clauses capture frequent patterns with high discriminating power, providing increasing expression power with each additional clause. However, the resulting accuracy gain comes at the cost of linear growth in computation time and memory usage. In this paper, we present the Weighted Tsetlin Machine (WTM), which reduces computation time and memory usage by \emph{weighting} the clauses. Real-valued weighting allows one clause to replace multiple and supports fine-tuning the impact of each clause. Our novel scheme simultaneously learns both the composition of the clauses and their weights. Furthermore, we increase training efficiency by replacing $k$ Bernoulli trials of success probability $p$ with a uniform sample of average size $p k$, the size drawn from a binomial distribution. In our empirical evaluation, the WTM achieved the same accuracy as the TM on MNIST, IMDb, and Connect-4, requiring only $1/4$, $1/3$, and $1/50$ of the clauses, respectively. With the same number of clauses, the WTM outperformed the TM, obtaining peak test accuracies of respectively $98.58\%$, $90.15\%$, and $87.49\%$. Finally, our novel sampling scheme reduced sample generation time by a factor of $7$.

Existing generalization theories analyze the generalization performance mainly based on the model complexity and training process. The ignorance of the task properties, which results from the widely used IID assumption, makes these theories fail to interpret many generalization phenomena or guide practical learning tasks. In this paper, we propose a new Independent and Task-Identically Distributed (ITID) assumption, to consider the task properties into the data generating process. The derived generalization bound based on the ITID assumption identifies the significance of hypothesis invariance in guaranteeing generalization performance. Based on the new bound, we introduce a practical invariance enhancement algorithm from the perspective of modifying data distributions. Finally, we verify the algorithm and theorems in the context of image classification task on both toy and real-world datasets. The experimental results demonstrate the reasonableness of the ITID assumption and the effectiveness of new generalization theory in improving practical generalization performance.

As a metric to measure the performance of an online method, dynamic regret with switching cost has drawn much attention for online decision making problems. Although the sublinear regret has been provided in many previous researches, we still have little knowledge about the relation between the dynamic regret and the switching cost. In the paper, we investigate the relation for two classic online settings: Online Algorithms (OA) and Online Convex Optimization (OCO). We provide a new theoretical analysis framework, which shows an interesting observation, that is, the relation between the switching cost and the dynamic regret is different for settings of OA and OCO. Specifically, the switching cost has significant impact on the dynamic regret in the setting of OA. But, it does not have an impact on the dynamic regret in the setting of OCO. Furthermore, we provide a lower bound of regret for the setting of OCO, which is same with the lower bound in the case of no switching cost. It shows that the switching cost does not change the difficulty of online decision making problems in the setting of OCO.

The importance of incorporating ethics and legal compliance into machine-assisted decision-making is broadly recognized. Further, several lines of recent work have argued that critical opportunities for improving data quality and representativeness, controlling for bias, and allowing humans to oversee and impact computational processes are missed if we do not consider the lifecycle stages upstream from model training and deployment. Yet, very little has been done to date to provide system-level support to data scientists who wish to develop and deploy responsible machine learning methods. We aim to fill this gap and present FairPrep, a design and evaluation framework for fairness-enhancing interventions. FairPrep is based on a developer-centered design, and helps data scientists follow best practices in software engineering and machine learning. As part of our contribution, we identify shortcomings in existing empirical studies for analyzing fairness-enhancing interventions. We then show how FairPrep can be used to measure the impact of sound best practices, such as hyperparameter tuning and feature scaling. In particular, our results suggest that the high variability of the outcomes of fairness-enhancing interventions observed in previous studies is often an artifact of a lack of hyperparameter tuning. Further, we show that the choice of a data cleaning method can impact the effectiveness of fairness-enhancing interventions.

We consider the problem of learning linear prediction models with model misspecification bias. In such case, the collinearity among input variables may inflate the error of parameter estimation, resulting in instability of prediction results when training and test distributions do not match. In this paper we theoretically analyze this fundamental problem and propose a sample reweighting method that reduces collinearity among input variables. Our method can be seen as a pretreatment of data to improve the condition of design matrix, and it can then be combined with any standard learning method for parameter estimation and variable selection. Empirical studies on both simulation and real datasets demonstrate the effectiveness of our method in terms of more stable performance across different distributed data.

Free-riders in Federated Learning: Attacks and Defenses Jierui Lin, Min Du, and Jian Liu University of California, Berkeley Abstract--Federated learning is a recently proposed paradigm that enables multiple clients to collaboratively train a joint model. It allows clients to train models locally, and leverages the parameter server to generate a global model by aggregating the locally submitted gradient updates at each round. Although the incentive model for federated learning has not been fully developed, it is supposed that participants are able to get rewards or the privilege to use the final global model, as a compensation for taking efforts to train the model. Therefore, a client who does not have any local data has the incentive to construct local gradient updates in order to deceive for rewards. In this paper, we are the first to propose the notion of free rider attacks, to explore possible ways that an attacker may construct gradient updates, without any local training data. Furthermore, we explore possible defenses that could detect the proposed attacks, and propose a new high dimensional detection method called STD-DAGMM, which particularly works well for anomaly detection of model parameters. We extend the attacks and defenses to consider more free riders as well as differential privacy, which sheds light on and calls for future research in this field. I NTRODUCTION F EDERA TED learning [1], [2], [3] has been proposed to facilitate a joint model training leveraging data from multiple clients, where the training process is coordinated by a parameter server. In the whole process, clients' data stay local, and only model parameters are communicated among clients through the parameter server. A typical training iteration works as follows. First, the parameter server sends the newest global model to each client. Then, each client locally updates the model using local data and reports updated gradients to the parameter server. Finally, the server performs model aggregation on all submitted local updates to form a new global model, which has better performance than models trained using any single client's data. Compared with an alternative approach which simply collects all data from the clients and trains a model on those data, federated learning is able to save the communication overhead by only transmitting model parameters, as well as protect privacy since all data stay local.