Minimum description length, regularisation and multi-modal data

Relationships between clustering, description length, and regularisation are pointed out, motivating the introduction of a cost function with a description length interpretation and the unusual and useful property of having its minimum approximated by the densest mode of a distribution. A simple inverse kinematics example is used to demonstrate that this property can be used to select and learn one branch of a multi-valued mapping. This property is also used to develop a method for setting regularisation parameters according to the scale on which structure is exhibited in the training data. The regularisation technique is demonstrated on two real data sets, a classification problem and a regression problem.

Minimum description length, regularisation and multi-modal data

Conventional feed forward Neural Networks have used the sum-of-squares cost function for training. A new cost function is presented here with a description length interpretation based on Rissanen's Minimum Description Length principle. It is a heuristic that has a rough interpretation as the number of data points fit by the model. Not concerned with finding optimal descriptions, the cost function prefers to form minimum descriptions in a naive way for computational convenience. The cost function is called the Naive Description Length cost function. Finding minimum description models will be shown to be closely related to the identification of clusters in the data. As a consequence the minimum of this cost function approximates the most probable mode of the data rather than the sum-of-squares cost function that approximates the mean. The new cost function is shown to provide information about the structure of the data. This is done by inspecting the dependence of the error to the amount of regularisation. This structure provides a method of selecting regularisation parameters as an alternative or supplement to Bayesian methods. The new cost function is tested on a number of multi-valued problems such as a simple inverse kinematics problem. It is also tested on a number of classification and regression problems. The mode-seeking property of this cost function is shown to improve prediction in time series problems. Description length principles are used in a similar fashion to derive a regulariser to control network complexity.

A comparison of the vocational training system of Britain and West Germany as experienced by minimum-age school leavers.

The sectoral and occupational structure of Britain and West Germany has increasingly changed over the last fifty years from a manual manufacturing based to a non-manual service sector based one. There has been a trend towards more managerial and less menial type occupations. Britain employs a higher proportion of its population in the service sector than in manufacturing compared to West Germany, except in retailing, where West Germany employs twice as many people as Britain. This is a stable sector of the economy in terms of employment, but the requirements of the workforce have changed in line with changes in the industry in both countries. School leavers in the two countries, faced with the same options (FE, training schemes or employment) have opted for the various options in different proportions: young Germans are staying longer in education before embarking on training and young Britons are now less likely to go straight into employment than ten years ago. Training is becoming more accepted as the normal route into employment with government policy leading the way, but public opinion still slow to respond. This study investigates how vocational training has adapted to the changing requirements of industry, often determined by technological advancements. In some areas e.g. manufacturing industry the changes have been radical, in others such as retailing they have not, but skill requirements, not necessarily influenced by technology have changed. Social-communicative skills, frequently not even considered skills and therefore not included in training are coming to the forefront. Vocational training has adapted differently in the two countries: in West Germany on the basis of an established over-defined system and in Britain on the basis of an out-dated ill-defined and almost non-existent system. In retailing German school leavers opt for two or three year apprenticeships whereas British school leavers are offered employment with or without formalised training. The publicly held view of the occupation of sales assistant is one of low-level skill, low intellectual demands and a job anyone can do. The traditional skills - product knowledge, selling and social-communicative skills have steadily been eroded. In the last five years retailers have recognised that a return to customer service, utilising the traditional skills was going to be needed of their staff to remain competitive. This requires training. The German retail training system responded by adapting its training regulations in a long consultative process, whereas the British experimented with YTS, a formalised training scheme nationwide being a new departure. The thesis evaluates the changes in these regulations. The case studies in four retail outlets demonstrate that it is indeed product knowledge and selling and social-communicative skills which are fundamental to being a successful and content sales assistant in either country. When the skills are recognised and taught well and systematically the foundations for career development in retailing are laid in a labour market which is continually looking for better qualified workers. Training, when planned and conducted professionally is appreciated by staff and customers and of benefit to the company. In retailing not enough systematic training, to recognisable standards is carried out in Britain, whereas in West Germany the training system is nevertheless better prepared to show innovative potential as a structure and is in place on which to build. In Britain the reputation of the individual company has a greater role to play, not ensuring a national provision of good training in retailing.

Optical link design for minimum power consumption and maximum capacity

Using a well-established analytic nonlinear signal-to-noise ratio noise model we show that there are very simple, fibre independent, amplifier gains which minimize the total energy requirement for amplified systems. Power savings of over 50% are shown to be possible by choosing appropriate amplifier gain and output power.

Minimum Mean Square Error Approach in Images Processing for Full-field Displacements and Deformation Measurements

A vision system is applied to full-field displacements and deformation measurements in solid mechanics. A speckle like pattern is preliminary formed on the surface under investigation. To determine displacements field of one speckle image with respect to a reference speckle image, sub-images, referred to Zones Of Interest (ZOI) are considered. The field is obtained by matching a ZOI in the reference image with the respective ZOI in the moved image. Two image processing techniques are used for implementing the matching procedure: – cross correlation function and minimum mean square error (MMSE) of the ZOI intensity distribution. The two algorithms are compared and the influence of the ZOI size on the accuracy of measurements is studied.

Multi-model fitting based on minimum spanning tree

This paper presents a novel approach to the computation of primitive geometrical structures, where no prior knowledge about the visual scene is available and a high level of noise is expected. We based our work on the grouping principles of proximity and similarity, of points and preliminary models. The former was realized using Minimum Spanning Trees (MST), on which we apply a stable alignment and goodness of fit criteria. As for the latter, we used spectral clustering of preliminary models. The algorithm can be generalized to various model fitting settings, without tuning of run parameters. Experiments demonstrate the significant improvement in the localization accuracy of models in plane, homography and motion segmentation examples. The efficiency of the algorithm is not dependent on fine tuning of run parameters like most others in the field.

Minimum Description Length Principle in Discriminating Marginal Distributions

2010 Mathematics Subject Classification: 94A17, 62B10, 62F03.

On the peculiar relevance of a fundamental dilemma of minimum-wage regulation in post-socialism – apropos of an international investigation

To the extent minimum-wage regulation is effective in fighting against excessive earnings handicaps of those at the lower end-tail of earnings distribution, it may have the side-effect of worsening their employment prospects. A demand-and-supply interpretation of data on the relative employment rate and earnings position of the least educated in the EU27 suggests that the resulting dilemma might be particularly relevant for minimum-wage policies in post-socialist countries.

"Minimálbér-paradoxon" versenyzői munkaerőpiacon? ("Minimum-wage paradox" in a competitive labour market? Lessons from an experimental line of thought)

A versenyzői munkaerőpiac hagyományos kereslet-kínálati modellje az egyensúlyi bérszintet meghaladó minimálbér következményeként az egyensúlyi bérszint mellettinél alacsonyabb foglalkoztatást jósol; minél magasabb a minimálbér, annál alacsonyabbat. Empirikus vizsgálatok szerint ugyanakkor a minimálbér-emelés nem feltétlenül csökkenti a foglalkoztatást - ezt nevezik minimálbér-paradoxonnak -, ami legkézenfekvőbben a munkáltatók munkaerő-piaci monopszonerejével látszik magyarázhatónak. Ezzel szemben az a gondolatkísérlet, amelyről ez a cikk beszámol, általánosabb érvényű, versenyzői munkaerőpiacot feltételező magyarázat kidolgozására irányul. / === / In the conventional textbook demand/supply model of competitive labour markets, the introduction of a minimum wage above market-clearing level must reduce employment. Empirical findings suggest, however, that this may not always be the case, a finding most readily explained by monopsonistic competition in the labour market. The experimental line of thought reported here explores an alternative root, interpreting the "minimum-wage paradox" as the outcome of a competitive labour market that displays friction.

A magyar minimálbér-szabályozás és hatása a foglalkoztatásra, különösen 2000-től napjainkig (Minimum-wage regulation in Hungary and its impact on employment, with particular respect to the 2000’s)

Noha az 1990-es évek első felében felbomlott az akadémiai közgazdászok sok évtizeden át örök érvényűnek hitt közmegegyezése a minimálbér szükségképpen negatív foglalkoztatási hatásáról, a túlságosan magas minimálbért minden közgazdász foglalkoztatáscsökkentő hatásúnak jósolja. Tanulmányunkban a magyar minimálbér-szabályozást e hatás szempontjából vizsgáljuk és értékeljük. / === / Although the long-held view of an unambiguously negative employment effect of a binding minimum wage was challenged by empirical findings in the early 1990’s, it is unanimously predicted that if the minimum wage is set too high it will bring about adverse employment effects. Accordingly, our study starts from an evaluation of the magnitude of the Hungarian minimum wage, i.e., of how it relates to minimum wage rates elsewhere, and of how it has developed through time. Next we inspect the main features that characterize the Hungarian system of minimum wage regulation. Theoretical views on the potential employment effect of minimum wage regulation are then surveyed and contrasted to empirical findings. The study concludes by policy recommendations. To sum up the main strand of arguments, we try to demonstrate that even though Hungary’s minimum wage, if assessed by its ratio to average and/or median full-time earnings, does not appear particularly high by international standards, it might rightly be regarded as unreasonably high in light of Hungary’s excessively low relative rate of employment among the least schooled. This diagnose should become particularly evident once one takes into account that, in sharp contrast to established rules elsewhere, a significantly higher wage floor is in effect for those with lower secondary schooling. Abolition of this legally guaranteed premium over the minimum wage as well as more moderation in minimum wage adjustments are thus highly recommended.

A minimálbér költségvetési hatásai = The budgetary effects of the minimum wage

A minimálbér-emelés a munkapiacon közvetlenül hat a keresletre és a kínálatra. Közvetett hatásai azonban túlmutatnak a munkapiacon, ezért azokat egy makromodell keretei között elemezzük. A makromodellben háromféle munkafajta és tíz ágazat van; az egyes ágazatok az árképzésükben és az adó- és járulékelkerülésük szerkezetében különböznek. A minimálbér-emelés munkapiaci feszültséget generál: csökkenti a foglalkoztatást a szakképzetlenek körében. Mivel az árszint az átlagbérnél gyorsabban nő, és az aggregált foglalkoztatás is csökken, így csökken a reálfogyasztás. A vállalatok profitja és beruházása csökken, ugyanakkor a vállalati profit csökkenése már csekély mértékű adóelkerülés-növeléssel is kiegyensúlyozható. A minimálbér-emelés hatására nőnek ugyan az adóbevételek, viszont a kiadások nagyobb mértékben nőnek, így általában romlik az egyenleg. Aki tehát a minimálbér emelését követeli, annak a felelős döntés során számolnia kell ezekkel a következményekkel. _____ Raising the minimum wage on the labour market has direct effects on supply and demand. But its indirect effects extend beyond the labour market. They are analysed here with a macro model that distinguishes three types of work and ten industries, whose firms differ in their price structures and the degrees to which tax and social-insurance payments are avoided. Raising the minimum wage generates tension on the labour market and reduces employment of the unskilled. Since the price level rises faster than average pay and aggregate employment falls, so does real consumption. The firms’ profits and investment decline, but the former can be offset even by a small increase in tax avoidance. Although the rise in the minimum wage boosts tax revenues, budgetary expenditures rise more and the balance deteriorates. Advocates of a higher minimum wage need to consider these consequences if they are to reach a responsible decision.