title: Learning from batched data: model combination vs data combination

authors: Ting, Kai Ming

subjects: computer science

abstract: When presented with multiple batches of data, one can either combine them into a single batch before applying a machine learning procedure or learn from each batch independently and combine the resulting models. The former procedure, data combination, is straightforward; this paper investigates the latter, model combination. Given an appropriate combination method, one might expect model combination to prove superior when the data in each batch was obtained under somewhat different conditions or when different learning algorithms were used on the batches. Empirical results show that model combination often outperforms data combination even when the batches are drawn randomly from a single source of data and the same learning method is used on each. Moreover, this is not just an artifact of one particular method of combining models: it occurs with several different combination methods. 
We relate this phenomenon to the learning curve of the classifiers being used. Early in the learning process when the learning curve is steep there is much to gain from data combination, but later when it becomes shallow there is less to gain and model combination achieves a greater reduction in variance and hence a lower error rate.
The practical implication of these results is that one should consider using model combination rather than data combination, especially when multiple batches of data for the same task are readily available. It is often superior even when the batches are drawn randomly from a single sample, and we expect its advantage to increase if genuine statistical differences between the batches exist.

text: Learning from batched data: model combination vs data combination When presented with multiple batches of data, one can either combine them into a single batch before applying a machine learning procedure or learn from each batch independently and combine the resulting models. The former procedure, data combination, is straightforward; this paper investigates the latter, model combination. Given an appropriate combination method, one might expect model combination to prove superior when the data in each batch was obtained under somewhat different conditions or when different learning algorithms were used on the batches. Empirical results show that model combination often outperforms data combination even when the batches are drawn randomly from a single source of data and the same learning method is used on each. Moreover, this is not just an artifact of one particular method of combining models: it occurs with several different combination methods. 
We relate this phenomenon to the learning curve of the classifiers being used. Early in the learning process when the learning curve is steep there is much to gain from data combination, but later when it becomes shallow there is less to gain and model combination achieves a greater reduction in variance and hence a lower error rate.
The practical implication of these results is that one should consider using model combination rather than data combination, especially when multiple batches of data for the same task are readily available. It is often superior even when the batches are drawn randomly from a single sample, and we expect its advantage to increase if genuine statistical differences between the batches exist.

year: 1997-05

title: The use of negative penalty functions in linear systems of equations

authors: Askes, Harm

subjects: constraint

abstract: Contrary to what is commonly thought, it is possible to obtain convergent results with negative (rather than positive) penalty functions. This has been shown and proven on various occasions for vibration analysis, but in this contribution it will also be shown and proven for systems of linear equations subjected to one or more constraints. As a key ingredient in the developed arguments, a pseudo-force is identified as the derivative of the constrained degree of freedom with respect to the inverse of the penalty parameter. Since this pseudo-force can be proven to be constant for large absolute values of the penalty parameter, it follows that the exact solution is bounded by the results obtained with negative and positive penalty parameters. The mathematical proofs are presented and two examples are shown to illustrate the principles.

text: The use of negative penalty functions in linear systems of equations Contrary to what is commonly thought, it is possible to obtain convergent results with negative (rather than positive) penalty functions. This has been shown and proven on various occasions for vibration analysis, but in this contribution it will also be shown and proven for systems of linear equations subjected to one or more constraints. As a key ingredient in the developed arguments, a pseudo-force is identified as the derivative of the constrained degree of freedom with respect to the inverse of the penalty parameter. Since this pseudo-force can be proven to be constant for large absolute values of the penalty parameter, it follows that the exact solution is bounded by the results obtained with negative and positive penalty parameters. The mathematical proofs are presented and two examples are shown to illustrate the principles.

year: 2006

title: Culture and climate change: A study of future-proofing Māori tourism businesses

authors: Tawhai, Crystal Candace

subjects: culture

abstract: This thesis explores how prepared Māori tourism businesses are to adapt to climate change and how Māori values may influence the business's perception of responses to climate change. As climate impacts are growing in New Zealand, as a result of increasing extreme weather events, how can Māori tourism businesses protect their taonga (resources)? Taonga in the context of this study includes Māori values, lands, seas and their businesses. Furthermore, the literature indicates that Māori tourism significantly contributes to the economic, social and cultural wellbeing for Māori and wider New Zealand (NZ Māori Tourism, 2018). 
At a specific level, the study focuses on three Māori tourism businesses. Two of the businesses are North Island-based whānau-owned enterprises, one on Kāpiti Island and the other in Napier. The third is a hapū-owned business located in Kaikoura in the South Island. Drawing on kaupapa Māori frameworks built on Māori struggles for tino rangatiratanga and mana motuhake (self-determination), the study adheres to kaupapa Māori principles of carrying out research by Māori to benefit Māori. The primary data for the study was collected through semi-structured interviews with each of the businesses, taking care to ensure the cultural safety of the participants and using appropriate tikanga (protocol) in each interview. 

The findings of the study show that Māori tourism businesses are adapting to environmental changes but are unsure about the pace of climate change. The uncertainties are due to a lack of access to information and competing priorities within their businesses. The research also shows how decisions made by local government as well as business perceptions of local and central government institutions negatively impacts on the ability of businesses to adapt to climate change. While there were differences in the businesses’ treatment of science and scientific information, all of them prioritised Māori cultural values. Significantly, these values underpin all the activities of the businesses, including, environmental enhancement and protection. An emphasis on Māori values in facilitated partnerships between tourism businesses, government bodies, and other community stakeholders on co-designing climate change adaptation strategies can help the tourism sector to prepare for a changing climate.

text: Culture and climate change: A study of future-proofing Māori tourism businesses This thesis explores how prepared Māori tourism businesses are to adapt to climate change and how Māori values may influence the business's perception of responses to climate change. As climate impacts are growing in New Zealand, as a result of increasing extreme weather events, how can Māori tourism businesses protect their taonga (resources)? Taonga in the context of this study includes Māori values, lands, seas and their businesses. Furthermore, the literature indicates that Māori tourism significantly contributes to the economic, social and cultural wellbeing for Māori and wider New Zealand (NZ Māori Tourism, 2018). 
At a specific level, the study focuses on three Māori tourism businesses. Two of the businesses are North Island-based whānau-owned enterprises, one on Kāpiti Island and the other in Napier. The third is a hapū-owned business located in Kaikoura in the South Island. Drawing on kaupapa Māori frameworks built on Māori struggles for tino rangatiratanga and mana motuhake (self-determination), the study adheres to kaupapa Māori principles of carrying out research by Māori to benefit Māori. The primary data for the study was collected through semi-structured interviews with each of the businesses, taking care to ensure the cultural safety of the participants and using appropriate tikanga (protocol) in each interview. 

The findings of the study show that Māori tourism businesses are adapting to environmental changes but are unsure about the pace of climate change. The uncertainties are due to a lack of access to information and competing priorities within their businesses. The research also shows how decisions made by local government as well as business perceptions of local and central government institutions negatively impacts on the ability of businesses to adapt to climate change. While there were differences in the businesses’ treatment of science and scientific information, all of them prioritised Māori cultural values. Significantly, these values underpin all the activities of the businesses, including, environmental enhancement and protection. An emphasis on Māori values in facilitated partnerships between tourism businesses, government bodies, and other community stakeholders on co-designing climate change adaptation strategies can help the tourism sector to prepare for a changing climate.

year: 2020