Telstra has used open source machine learning technology to answer the age-old question that plagues every marketer: how effective is my ad spend? The telco wields one of the biggest marketing budgets in Australia, but that doesn't stop Telstra from wanting to track the performance of every dollar spent. The company previously faced a six-month lag to get visibility into the effectiveness of its marketing spend; that is now down to five weeks using new marketing mix modelling developed in partnership with Accenture, Deakin University and Servian. The telco previously used a traditional econometric model to assess the performance of its marketing spend, pulling together 800 variables – which took two-and-a-half months to assemble – and then modelling this using regression techniques. "Six months after the marketing period had ended I could tell the CMO [chief marketing officer] and the marketers how effective their marketing was... six months ago," Telstra's director of research, insights & analytics Liz Moore told the recent Big Data & Analytics Innovation Summit in Sydney.

We study parameter estimation in Nonlinear Factor Analysis (NFA) where the generative model is parameterized by a deep neural network. Recent work has focused on learning such models using inference (or recognition) networks; we identify a crucial problem when modeling large, sparse, high-dimensional datasets -- underfitting. We study the extent of underfitting, highlighting that its severity increases with the sparsity of the data. We propose methods to tackle it via iterative optimization inspired by stochastic variational inference \citep{hoffman2013stochastic} and improvements in the sparse data representation used for inference. The proposed techniques drastically improve the ability of these powerful models to fit sparse data, achieving state-of-the-art results on a benchmark text-count dataset and excellent results on the task of top-N recommendation.

In econometrics and finance, the vector error correction model (VECM) is an important time series model for cointegration analysis, which is used to estimate the long-run equilibrium variable relationships. The traditional analysis and estimation methodologies assume the underlying Gaussian distribution but, in practice, heavy-tailed data and outliers can lead to the inapplicability of these methods. In this paper, we propose a robust model estimation method based on the Cauchy distribution to tackle this issue. In addition, sparse cointegration relations are considered to realize feature selection and dimension reduction. An efficient algorithm based on the majorization-minimization (MM) method is applied to solve the proposed nonconvex problem. The performance of this algorithm is shown through numerical simulations.

But how can we train graphical models on a massive data set? In this paper, we show how to construct coresets--compressed data sets which can be used as proxy for the original data and have provably bounded worst case error--for Gaussian dependency networks (DNs), i.e., cyclic directed graphical models over Gaussians, where the parents of each variable are its Markov blanket. Specifically, we prove that Gaussian DNs admit coresets of size independent of the size of the data set. Unfortunately, this does not extend to DNs over members of the exponential family in general. As we will prove, Poisson DNs do not admit small coresets. Despite this worst-case result, we will provide an argument why our coreset construction for DNs can still work well in practice on count data. To corroborate our theoretical results, we empirically evaluated the resulting Core DNs on real data sets. The results demonstrate significant gains over no or naive sub-sampling, even in the case of count data.

Given data over the joint distribution of two random variables $X$ and $Y$, we consider the problem of inferring the most likely causal direction between $X$ and $Y$. In particular, we consider the general case where both $X$ and $Y$ may be univariate or multivariate, and of the same or mixed data types. We take an information theoretic approach, based on Kolmogorov complexity, from which it follows that first describing the data over cause and then that of effect given cause is shorter than the reverse direction. The ideal score is not computable, but can be approximated through the Minimum Description Length (MDL) principle. Based on MDL, we propose two scores, one for when both $X$ and $Y$ are of the same single data type, and one for when they are mixed-type. We model dependencies between $X$ and $Y$ using classification and regression trees. As inferring the optimal model is NP-hard, we propose Crack, a fast greedy algorithm to determine the most likely causal direction directly from the data. Empirical evaluation on a wide range of data shows that Crack reliably, and with high accuracy, infers the correct causal direction on both univariate and multivariate cause-effect pairs over both single and mixed-type data.

Inference in hidden Markov model has been challenging in terms of scalability due to dependencies in the observation data. In this paper, we utilize the inherent memory decay in hidden Markov models, such that the forward and backward probabilities can be carried out with subsequences, enabling efficient inference over long sequences of observations. We formulate this forward filtering process in the setting of the random dynamical system and there exist Lyapunov exponents in the i.i.d random matrices production. And the rate of the memory decay is known as $\lambda_2-\lambda_1$, the gap of the top two Lyapunov exponents almost surely. An efficient and accurate algorithm is proposed to numerically estimate the gap after the soft-max parametrization. The length of subsequences $B$ given the controlled error $\epsilon$ is $B=\log(\epsilon)/(\lambda_2-\lambda_1)$. We theoretically prove the validity of the algorithm and demonstrate the effectiveness with numerical examples. The method developed here can be applied to widely used algorithms, such as mini-batch stochastic gradient method. Moreover, the continuity of Lyapunov spectrum ensures the estimated $B$ could be reused for the nearby parameter during the inference.

This paper proposes a general method for improving the structure and quality of sequences generated by a recurrent neural network (RNN), while maintaining information originally learned from data, as well as sample diversity. An RNN is first pre-trained on data using maximum likelihood estimation (MLE), and the probability distribution over the next token in the sequence learned by this model is treated as a prior policy. Another RNN is then trained using reinforcement learning (RL) to generate higher-quality outputs that account for domain-specific incentives while retaining proximity to the prior policy of the MLE RNN. To formalize this objective, we derive novel off-policy RL methods for RNNs from KL-control. The effectiveness of the approach is demonstrated on two applications; 1) generating novel musical melodies, and 2) computational molecular generation. For both problems, we show that the proposed method improves the desired properties and structure of the generated sequences, while maintaining information learned from data.

So how do we determine the "best" decision? This requires that we first define some notion of what we want (what are we trying to do?). The formal object that we use to do this goes by many names depending on the field: I will refer to it as a Loss function (\(\mathcal{L}\)) but the same general concept may be alternatively called a cost function, a utility function, an acquisition function, or any number of different things. The crucial idea is that this is a function that allows us to quantify how bad/good a given decision (\(a\)) is given some information (\(\theta\)). What does it mean to quantify?

Using established principles from Information Theory and Statistics, we show that in a deep neural network invariance to nuisance factors is equivalent to information minimality of the learned representation, and that stacking layers and injecting noise during training naturally bias the network towards learning invariant representations. We then show that, in order to avoid memorization, we need to limit the quantity of information stored in the weights, which leads to a novel usage of the Information Bottleneck Lagrangian on the weights as a learning criterion. This also has an alternative interpretation as minimizing a PAC-Bayesian bound on the test error. Finally, we exploit a duality between weights and activations induced by the architecture, to show that the information in the weights bounds the minimality and Total Correlation of the layers, therefore showing that regularizing the weights explicitly or implicitly, using SGD, not only helps avoid overfitting, but also fosters invariance and disentangling of the learned representation. The theory also enables predicting sharp phase transitions between underfitting and overfitting random labels at precise information values, and sheds light on the relation between the geometry of the loss function, in particular so-called "flat minima," and generalization.

Pair Hidden Markov Models (PHMMs) are probabilistic models used for pairwise sequence alignment, a quintessential problem in bioinformatics. PHMMs include three types of hidden states: match, insertion and deletion. Most previous studies have used one or two hidden states for each PHMM state type. However, few studies have examined the number of states suitable for representing sequence data or improving alignment accuracy.We developed a novel method to select superior models (including the number of hidden states) for PHMM. Our method selects models with the highest posterior probability using Factorized Information Criteria (FIC), which is widely utilised in model selection for probabilistic models with hidden variables. Our simulations indicated this method has excellent model selection capabilities with slightly improved alignment accuracy. We applied our method to DNA datasets from 5 and 28 species, ultimately selecting more complex models than those used in previous studies.