Due to unmeasured confounding, it is often not possible to identify causal effects from a postulated model. Nevertheless, we can ask for partial identification, which usually boils down to finding upper and lower bounds of a causal quantity of interest derived from all solutions compatible with the encoded structural assumptions. One appealing way to derive such bounds is by casting it in terms of a constrained optimization method that searches over all causal models compatible with evidence, as introduced in the classic work of Balke and Pearl (1994) for discrete data. Although by construction this guarantees tight bounds, it poses a formidable computational challenge. To cope with this issue, alternatives include algorithms that are not guaranteed to be tight, or by introducing restrictions on the class of models. In this paper, we introduce a novel alternative: inspired by ideas coming from belief propagation, we enforce compatibility between marginals of a causal model and data, without constructing a global causal model. We call this collection of locally consistent marginals the causal marginal polytope. As global independence constraints disappear when considering small dimensional tractable marginals, this also leads to a rethinking of how to elicit and express causal knowledge. We provide an explicit algorithm and implementation of this idea, and assess its practicality with numerical experiments.

We develop a mixtures-of-experts (ME) approach to the multiclass classification where the predictors are univariate functions. It consists of a ME model in which both the gating network and the experts network are constructed upon multinomial logistic activation functions with functional inputs. We perform a regularized maximum likelihood estimation in which the coefficient functions enjoy interpretable sparsity constraints on targeted derivatives. We develop an EM-Lasso like algorithm to compute the regularized MLE and evaluate the proposed approach on simulated and real data.

In the moment between reading a phone number and punching it into your phone, you may find that the digits have mysteriously gone astray--even if you've seared the first ones into your memory, the last ones may still blur unaccountably. Was the 6 before the 8 or after it? Maintaining such scraps of information long enough to act on them draws on an ability called visual working memory. For years, scientists have debated whether working memory has space for only a few items at a time or if it just has limited room for detail: Perhaps our mind's capacity is spread across either a few crystal-clear recollections or a multitude of more dubious fragments. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

This article was published as a part of the Data Science Blogathon. Mobile phones come in all sorts of prices, features, specifications and all. Price estimation and prediction is an important part of consumer strategy. Deciding on the correct price of a product is very important for the market success of a product. A new product that has to be launched, must have the correct price so that consumers find it appropriate to buy the product.

In this paper, we study the controllability of an Expressive TTS system trained on a dataset for a continuous control. The dataset is the Blizzard 2013 dataset based on audiobooks read by a female speaker containing a great variability in styles and expressiveness. Controllability is evaluated with both an objective and a subjective experiment. The objective assessment is based on a measure of correlation between acoustic features and the dimensions of the latent space representing expressiveness. The subjective assessment is based on a perceptual experiment in which users are shown an interface for Controllable Expressive TTS and asked to retrieve a synthetic utterance whose expressiveness subjectively corresponds to that a reference utterance.

In machine learning, crowdsourcing is an economical way to label a large amount of data. However, the noise in the produced labels may deteriorate the accuracy of any classification method applied to the labelled data. We propose an enhanced nearest neighbor classifier (ENN) to overcome this issue. Two algorithms are developed to estimate the worker quality (which is often unknown in practice): one is to construct the estimate based on the denoised worker labels by applying the $k$NN classifier to the expert data; the other is an iterative algorithm that works even without access to the expert data. Other than strong numerical evidence, our proposed methods are proven to achieve the same regret as its oracle version based on high-quality expert data. As a technical by-product, a lower bound on the sample size assigned to each worker to reach the optimal convergence rate of regret is derived.

Frequentist and Bayesian are two different versions of statistics. Frequentist is a more classical version, which, as the name suggests, rely on the long run frequency of events (data points) to calculate the variable of interest. Bayesian on the other hand, can also work without having a large number of events (in fact, it could work even with one data point!). The cardinal difference between the two is that: frequentist will give you a point estimate, whereas Bayesian will give you a distribution. Having a point estimate means that -- "we are certain that this is the output for this variable of interest". Whereas, having a distribution can be interpreted as -- "we have some belief that the mean of the distribution is the good estimate for this variable of interest, but there is uncertainty too, in the form of standard deviation".

Increased Internet speeds and advanced technology means data science is high in demand. According to Glassdoor, a career as a data scientist is the third-best job in the United States for 2022. This increase in popularity means that all IT professionals, and aspiring professionals, should be familiar with our list of data science terms. For those looking to become a data scientist, in-depth knowledge of both basic and advanced data science terminology is vital. Our glossary of data science terminology will act as a data science terminology cheat sheet of basic and advanced terms as you start your journey as a data scientist.

Despite numerous studies of deep autoencoders (AEs) for unsupervised anomaly detection, AEs still lack a way to express uncertainty in their predictions, crucial for ensuring safe and trustworthy machine learning systems in high-stake applications. Therefore, in this work, the formulation of Bayesian autoencoders (BAEs) is adopted to quantify the total anomaly uncertainty, comprising epistemic and aleatoric uncertainties. To evaluate the quality of uncertainty, we consider the task of classifying anomalies with the additional option of rejecting predictions of high uncertainty. In addition, we use the accuracy-rejection curve and propose the weighted average accuracy as a performance metric. Our experiments demonstrate the effectiveness of the BAE and total anomaly uncertainty on a set of benchmark datasets and two real datasets for manufacturing: one for condition monitoring, the other for quality inspection.

Dynamic mechanism design studies how mechanism designers should allocate resources among agents in a time-varying environment. We consider the problem where the agents interact with the mechanism designer according to an unknown Markov Decision Process (MDP), where agent rewards and the mechanism designer's state evolve according to an episodic MDP with unknown reward functions and transition kernels. We focus on the online setting with linear function approximation and attempt to recover the dynamic Vickrey-Clarke-Grove (VCG) mechanism over multiple rounds of interaction. A key contribution of our work is incorporating reward-free online Reinforcement Learning (RL) to aid exploration over a rich policy space to estimate prices in the dynamic VCG mechanism. We show that the regret of our proposed method is upper bounded by $\tilde{\mathcal{O}}(T^{2/3})$ and further devise a lower bound to show that our algorithm is efficient, incurring the same $\tilde{\mathcal{O}}(T^{2 / 3})$ regret as the lower bound, where $T$ is the total number of rounds. Our work establishes the regret guarantee for online RL in solving dynamic mechanism design problems without prior knowledge of the underlying model.