Order effects occur when judgments about a hypothesis's probability given a sequence of information do not equal the probability of the same hypothesis when the information is reversed. Different experiments have been performed in the literature that supports evidence of order effects. We proposed a Bayesian update model for order effects where each question can be thought of as a mini-experiment where the respondents reflect on their beliefs. We showed that order effects appear, and they have a simple cognitive explanation: the respondent's prior belief that two questions are correlated. The proposed Bayesian model allows us to make several predictions: (1) we found certain conditions on the priors that limit the existence of order effects; (2) we show that, for our model, the QQ equality is not necessarily satisfied (due to symmetry assumptions); and (3) the proposed Bayesian model has the advantage of possessing fewer parameters than its quantum counterpart.
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Large pretrained language models such as GPT-3 have the surprising ability to do in-context learning, where the model learns to do a downstream task simply by conditioning on a prompt consisting of input-output examples. Without being explicitly pretrained to do so, the language model learns from these examples during its forward pass without parameter updates on "out-of-distribution" prompts. Thus, it is unclear what mechanism enables in-context learning. In this paper, we study the role of the pretraining distribution on the emergence of in-context learning under a mathematical setting where the pretraining texts have long-range coherence. Here, language model pretraining requires inferring a latent document-level concept from the conditioning text to generate coherent next tokens. At test time, this mechanism enables in-context learning by inferring the shared latent concept between prompt examples and applying it to make a prediction on the test example. Concretely, we prove that in-context learning occurs implicitly via Bayesian inference of the latent concept when the pretraining distribution is a mixture of HMMs. This can occur despite the distribution mismatch between prompts and pretraining data. In contrast to messy large-scale pretraining datasets for in-context learning in natural language, we generate a family of small-scale synthetic datasets (GINC) where Transformer and LSTM language models both exhibit in-context learning. Beyond the theory which focuses on the effect of the pretraining distribution, we empirically find that scaling model size improves in-context accuracy even when the pretraining loss is the same.
We establish theoretical results about the low frequency contamination (i.e., long memory effects) induced by general nonstationarity for estimates such as the sample autocovariance and the periodogram, and deduce consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We present explicit expressions for the asymptotic bias of these estimates. We distinguish cases where this contamination only occurs as a small-sample problem and cases where the contamination continues to hold asymptotically. We show theoretically that nonparametric smoothing over time is robust to low frequency contamination. Our results provide new insights on the debate between consistent versus inconsistent long-run variance (LRV) estimation. Existing LRV estimators tend to be in inflated when the data are nonstationary. This results in HAR tests that can be undersized and exhibit dramatic power losses. Our theory indicates that long bandwidths or fixed-b HAR tests suffer more from low frequency contamination relative to HAR tests based on HAC estimators, whereas recently introduced double kernel HAC estimators do not super from this problem. Finally, we present second-order Edgeworth expansions under nonstationarity about the distribution of HAC and DK-HAC estimators and about the corresponding t-test in the linear regression model.
Many popular specifications for Vector Autoregressions (VARs) with multivariate stochastic volatility are not invariant to the way the variables are ordered due to the use of a Cholesky decomposition for the error covariance matrix. We show that the order invariance problem in existing approaches is likely to become more serious in large VARs. We propose the use of a specification which avoids the use of this Cholesky decomposition. We show that the presence of multivariate stochastic volatility allows for identification of the proposed model and prove that it is invariant to ordering. We develop a Markov Chain Monte Carlo algorithm which allows for Bayesian estimation and prediction. In exercises involving artificial and real macroeconomic data, we demonstrate that the choice of variable ordering can have non-negligible effects on empirical results. In a macroeconomic forecasting exercise involving VARs with 20 variables we find that our order-invariant approach leads to the best forecasts and that some choices of variable ordering can lead to poor forecasts using a conventional, non-order invariant, approach.
This paper considers the inference for heterogeneous treatment effects in dynamic settings that covariates and treatments are longitudinal. We focus on high-dimensional cases that the sample size, $N$, is potentially much larger than the covariate vector's dimension, $d$. The marginal structural mean models are considered. We propose a "sequential model doubly robust" estimator constructed based on "moment targeted" nuisance estimators. Such nuisance estimators are carefully designed through non-standard loss functions, reducing the bias resulting from potential model misspecifications. We achieve $\sqrt N$-inference even when model misspecification occurs. We only require one nuisance model to be correctly specified at each time spot. Such model correctness conditions are weaker than all the existing work, even containing the literature on low dimensions.
Distributional reinforcement learning (RL) -- in which agents learn about all the possible long-term consequences of their actions, and not just the expected value -- is of great recent interest. One of the most important affordances of a distributional view is facilitating a modern, measured, approach to risk when outcomes are not completely certain. By contrast, psychological and neuroscientific investigations into decision making under risk have utilized a variety of more venerable theoretical models such as prospect theory that lack axiomatically desirable properties such as coherence. Here, we consider a particularly relevant risk measure for modeling human and animal planning, called conditional value-at-risk (CVaR), which quantifies worst-case outcomes (e.g., vehicle accidents or predation). We first adopt a conventional distributional approach to CVaR in a sequential setting and reanalyze the choices of human decision-makers in the well-known two-step task, revealing substantial risk aversion that had been lurking under stickiness and perseveration. We then consider a further critical property of risk sensitivity, namely time consistency, showing alternatives to this form of CVaR that enjoy this desirable characteristic. We use simulations to examine settings in which the various forms differ in ways that have implications for human and animal planning and behavior.
In this paper we have to demonstrate that if we claim to have an algorithm that solves CSAT in polynomial time with a DTM (Deterministic Turing Machine), then we have to admit that: there is a counterexample that invalidates the correctness of the algorithm. This is because if we suppose that it can prove that an elenkhos formula (a formula that lists the negated codes of all models) is a contradiction, and if we change exactly a specific boolean variable of that formula, then we have proven that: in this case the algorithm will always fail.
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.
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.
Most existing work on automated fact checking is concerned with predicting the veracity of claims based on metadata, social network spread, language used in claims, and, more recently, evidence supporting or denying claims. A crucial piece of the puzzle that is still missing is to understand how to automate the most elaborate part of the process -- generating justifications for verdicts on claims. This paper provides the first study of how these explanations can be generated automatically based on available claim context, and how this task can be modelled jointly with veracity prediction. Our results indicate that optimising both objectives at the same time, rather than training them separately, improves the performance of a fact checking system. The results of a manual evaluation further suggest that the informativeness, coverage and overall quality of the generated explanations are also improved in the multi-task model.
Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space, such as the simplex, the time-discretisation error can dominate when we are near the boundary of the space. We demonstrate that while current SGMCMC methods for the simplex perform well in certain cases, they struggle with sparse simplex spaces; when many of the components are close to zero. However, most popular large-scale applications of Bayesian inference on simplex spaces, such as network or topic models, are sparse. We argue that this poor performance is due to the biases of SGMCMC caused by the discretization error. To get around this, we propose the stochastic CIR process, which removes all discretization error and we prove that samples from the stochastic CIR process are asymptotically unbiased. Use of the stochastic CIR process within a SGMCMC algorithm is shown to give substantially better performance for a topic model and a Dirichlet process mixture model than existing SGMCMC approaches.
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