Establishing the invariance property of an instrument (e.g., a questionnaire or test) is a key step for establishing its measurement validity. Measurement invariance is typically assessed by differential item functioning (DIF) analysis, i.e., detecting DIF items whose response distribution depends not only on the latent trait measured by the instrument but also the group membership. DIF analysis is confounded by the group difference in the latent trait distributions. Many DIF analyses require to know several anchor items that are DIF-free and then draw inference on whether each of the rest is a DIF item, where the anchor items are used to calibrate the latent trait distributions. In this paper, we propose a new method for DIF analysis under a multiple indicators and multiple causes (MIMIC) model for DIF. This method adopts a minimal L1 norm condition for identifying the latent trait distributions. It can not only accurately estimate the DIF effects of individual items without requiring prior knowledge about an anchor set, but also draw valid statistical inference, which yields accurate detection of DIF items. The inference results further allow us to control the type-I error for DIF detection. We conduct simulation studies to evaluate the performance of the proposed method and compare it with the anchor-set-based likelihood ratio test approach and the LASSO approach. The proposed method is further applied to analyzing the three personality scales of Eysenck personality questionnaire - revised (EPQ-R).
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We explore a hidden feedback loops effect in online recommender systems. Feedback loops result in degradation of online multi-armed bandit (MAB) recommendations to a small subset and loss of coverage and novelty. We study how uncertainty and noise in user interests influence the existence of feedback loops. First, we show that an unbiased additive random noise in user interests does not prevent a feedback loop. Second, we demonstrate that a non-zero probability of resetting user interests is sufficient to limit the feedback loop and estimate the size of the effect. Our experiments confirm the theoretical findings in a simulated environment for four bandit algorithms.
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker--Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation is required, e.g., for model evaluation and parameter fitting. However, the prescribed boundary conditions lead to a strong singularity and thus to slow convergence of numerical approximations. In this article we demonstrate that the solution can be related to the solution of a parabolic PDE on a rectangular space-time domain with homogeneous initial and boundary conditions by transformation and subtraction of a known function. We verify that the solution of the new PDE is indeed more regular than the solution of the original PDE and proceed to discretize the new PDE using a space-time minimal residual method. We also demonstrate that the solution depends analytically on the parameters determining the boundaries as well as the drift. This justifies the use of a sparse tensor product interpolation method to approximate the PDE solution for various parameter ranges. The predicted convergence rates of the minimal residual method and that of the interpolation method are supported by numerical simulations.
Multi-armed bandit algorithms like Thompson Sampling can be used to conduct adaptive experiments, in which maximizing reward means that data is used to progressively assign more participants to more effective arms. Such assignment strategies increase the risk of statistical hypothesis tests identifying a difference between arms when there is not one, and failing to conclude there is a difference in arms when there truly is one. We present simulations for 2-arm experiments that explore two algorithms that combine the benefits of uniform randomization for statistical analysis, with the benefits of reward maximization achieved by Thompson Sampling (TS). First, Top-Two Thompson Sampling adds a fixed amount of uniform random allocation (UR) spread evenly over time. Second, a novel heuristic algorithm, called TS PostDiff (Posterior Probability of Difference). TS PostDiff takes a Bayesian approach to mixing TS and UR: the probability a participant is assigned using UR allocation is the posterior probability that the difference between two arms is `small' (below a certain threshold), allowing for more UR exploration when there is little or no reward to be gained. We find that TS PostDiff method performs well across multiple effect sizes, and thus does not require tuning based on a guess for the true effect size.
We study a sound verification method for parametric component-based systems. The method uses a resource logic, a new formal specification language for distributed systems consisting of a finite yet unbounded number of components. The logic allows the description of architecture configurations coordinating instances of a finite number of types of components, by means of inductive definitions similar to the ones used to describe algebraic data types or recursive data structures. For parametric systems specified in this logic, we show that decision problems such as reaching deadlock or violating critical section are undecidable, in general. Despite this negative result, we provide for these decision problems practical semi-algorithms relying on the automatic synthesis of structural invariants allowing the proof of general safety properties. The invariants are defined using the WSkS fragment of the monadic second order logic, known to be decidable by a classical automata-logic connection, thus reducing a verification problem to checking satisfiability of a WSkS formula.
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible ways, often under the heading of approximate Bayesian computation or likelihood-free inference. There is, however, no consensus on how to rigorously evaluate the performance of these algorithms. Here, we argue for scoring algorithms by the mean squared error in estimating expectations of functions with respect to the posterior. We show that score implies common alternatives, including the acceptance rate and effective sample size, as limiting special cases. We then derive asymptotically optimal distributions for choosing or sampling discrete or continuous simulation parameters, respectively. Our recommendations differ significantly from guidelines based on alternative scores outside of their region of validity. As an application, we show sequential Monte Carlo in this context can be made more accurate with no new samples by accepting particles from all rounds.
To drive purchase in online advertising, it is of the advertiser's great interest to optimize the sequential advertising strategy whose performance and interpretability are both important. The lack of interpretability in existing deep reinforcement learning methods makes it not easy to understand, diagnose and further optimize the strategy. In this paper, we propose our Deep Intents Sequential Advertising (DISA) method to address these issues. The key part of interpretability is to understand a consumer's purchase intent which is, however, unobservable (called hidden states). In this paper, we model this intention as a latent variable and formulate the problem as a Partially Observable Markov Decision Process (POMDP) where the underlying intents are inferred based on the observable behaviors. Large-scale industrial offline and online experiments demonstrate our method's superior performance over several baselines. The inferred hidden states are analyzed, and the results prove the rationality of our inference.
The availability of large microarray data has led to a growing interest in biclustering methods in the past decade. Several algorithms have been proposed to identify subsets of genes and conditions according to different similarity measures and under varying constraints. In this paper we focus on the exclusive row biclustering problem for gene expression data sets, in which each row can only be a member of a single bicluster while columns can participate in multiple ones. This type of biclustering may be adequate, for example, for clustering groups of cancer patients where each patient (row) is expected to be carrying only a single type of cancer, while each cancer type is associated with multiple (and possibly overlapping) genes (columns). We present a novel method to identify these exclusive row biclusters through a combination of existing biclustering algorithms and combinatorial auction techniques. We devise an approach for tuning the threshold for our algorithm based on comparison to a null model in the spirit of the Gap statistic approach. We demonstrate our approach on both synthetic and real-world gene expression data and show its power in identifying large span non-overlapping rows sub matrices, while considering their unique nature. The Gap statistic approach succeeds in identifying appropriate thresholds in all our examples.
In this paper, we propose a novel sequence-aware recommendation model. Our model utilizes self-attention mechanism to infer the item-item relationship from user's historical interactions. With self-attention, it is able to estimate the relative weights of each item in user interaction trajectories to learn better representations for user's transient interests. The model is finally trained in a metric learning framework, taking both short-term and long-term intentions into consideration. Experiments on a wide range of datasets on different domains demonstrate that our approach outperforms the state-of-the-art by a wide margin.
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works have focused on fairness with respect to a specific metric, modeled the corresponding fair classification problem as a constrained optimization problem, and developed tailored algorithms to solve them. Despite this, there still remain important metrics for which we do not have fair classifiers and many of the aforementioned algorithms do not come with theoretical guarantees; perhaps because the resulting optimization problem is non-convex. The main contribution of this paper is a new meta-algorithm for classification that takes as input a large class of fairness constraints, with respect to multiple non-disjoint sensitive attributes, and which comes with provable guarantees. This is achieved by first developing a meta-algorithm for a large family of classification problems with convex constraints, and then showing that classification problems with general types of fairness constraints can be reduced to those in this family. We present empirical results that show that our algorithm can achieve near-perfect fairness with respect to various fairness metrics, and that the loss in accuracy due to the imposed fairness constraints is often small. Overall, this work unifies several prior works on fair classification, presents a practical algorithm with theoretical guarantees, and can handle fairness metrics that were previously not possible.
We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.
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